I've found an interesting suggestion in one of Civilization 2 guidelines (as I've already said before I read them as they are really useful for Civilization 1 as well, not completely but at least 70% and with some interpretation they can work for you very well).
One of the things I found is a rush build of military units (including settlers).
There are two major points there.
First of all we all know that it's just ridiculous to buy anything without any shields in the city screen (except under some really desperate circumstances but I'm not going to talk about them here). so, let's say you've got some shields.
First point is not to buy units as this way you would waste the shields produced at that turn. One suggestion if you still want (or have to) buy a unit, relocate your people to squares with less production but with more food or trade arrows, and once the unit is built, return them back.
Second one is instead of buying units, buy shields. Certainly you can't buy let's say 20 shields directly but there is a work around for that. Let's say you are building a settler (I would rather talk about settlers cause it is critical to build as many as possible within a shortest possible timeframe in the beginning of the game, so that you could found enough cities, connecting them with roads, and then start improving productive squares).
There is another reason to buy shields not units is the more shields you are buying the more expensive they are per shield.
As an example, you want to buy a diplomat (cost - 30 shields) and here is how much you would pay (1st column - how many shields you have in a city screen, 2nd - how many shields you are actually buying, 3rd - how much you would pay, 4th - price per shield) :
7 23 72 3.13
13 17 48 2.82
25 5 11 2.20
28 2 4 2.00
So, you can easily see that the less shields you are buying the better deal you get. If you buy from 1 to 4 shields you are paying the lowest possible rate - 2 coins per shield. So, for example you are building a settler (cost 40) and you have 26 shields in the city screen and your current city production is 2 shields per turn. Instead of buying a settler, switch to a diplomat (cost 30), buy it for 8 coins, switch back to a settler, and now you have 30 shields in the city screen. Next turn you will have 30+2=32, and then you'll build a settler in a few turns.
Let's have a look at other options.
Option 2 : buy it - it would cost you (as per my estimation) 39 coins and you would get a settler next turn.
Option 3 : just build it - seven turns, no money spent.
Option 4 : build it till it is cheap to buy it (i.e. till you have 36 shields in the city screen) , three turns and 8 coins.
So let's see what we have (1st column - how many turns it took to build a settler, 2nd - how much money spent) :
Option 1 : 5/8
Option 2 : 1/39
Option 3 : 7/0
Option 4 : 7/8
so, you can see that you can get a settler two turns earlier than via its normal production. And it is for a very reasonable price of 8 coins. Option 2 and especially option 4 is just a waste of money. Moreover if you do a switch-buy-switch back thing three times during production of the settler (when you have 16 coins in the city screen switch to a phalanx buy it and switch back to a settler, and before, when you have 6 - use a militia), you would save 6 turns. If you build 5 settlers this way, your total gain is 30 turns. Awesome.
All I said before was applicable to both Civilization 1 and 2. Now, something that can be done in Civilization 1 only. As you are not loosing shields when you switch between production of city improvements and military units you can buy units really cheap. Let's say you have 2 shields in the city screen, switch from the settler to a city improvement of the same price - a barracks or a temple. Buy it. It would cost you 72 coins, then switch back to your settler or e.g. chariot (I would also suggest moving people off the shield producing squares to food or trade arrow producing ones for this turn to minimize loss of produced shields). You'll get a unit next turn. If you bought it as a unit, you would have spent 152 coins (it is just my estimation - check it in the game but should be pretty close). So, the first option would save you 80 coins. Awesome.
Another use of this approach is to rush build caravans and then help to build wonders. Briefly : set a Caravan in production, wait one turn, switch to temple or barracks, buy it, switch back to a Caravan, your city have to produce 10 shields to complete it. If your city production is 5 shields, it would take 3 turns and 70 coins to build a Caravan. Normal production would take 10 turns. You bought 35 shields for 70 coins, if you did it for the wonder, you would spent 140 coins. In other words, you saved 70 coins per caravan, or from 420 to 840 coins per a wonder. Awesome.
The only drawback of the latest approach is that to be able to do it, you should have a temple or barracks still to be built. For settlers and wonders it works fine (normally you build those units in cities without barracks). Veteran units unfortunately can't produced this way (I build temples in each city so it's not an option for me) as you already should have barracks there. Anyway you can do iterations using cheaper units as I described in the first half of my post.
One of the things I found is a rush build of military units (including settlers).
There are two major points there.
First of all we all know that it's just ridiculous to buy anything without any shields in the city screen (except under some really desperate circumstances but I'm not going to talk about them here). so, let's say you've got some shields.
First point is not to buy units as this way you would waste the shields produced at that turn. One suggestion if you still want (or have to) buy a unit, relocate your people to squares with less production but with more food or trade arrows, and once the unit is built, return them back.
Second one is instead of buying units, buy shields. Certainly you can't buy let's say 20 shields directly but there is a work around for that. Let's say you are building a settler (I would rather talk about settlers cause it is critical to build as many as possible within a shortest possible timeframe in the beginning of the game, so that you could found enough cities, connecting them with roads, and then start improving productive squares).
There is another reason to buy shields not units is the more shields you are buying the more expensive they are per shield.
As an example, you want to buy a diplomat (cost - 30 shields) and here is how much you would pay (1st column - how many shields you have in a city screen, 2nd - how many shields you are actually buying, 3rd - how much you would pay, 4th - price per shield) :
7 23 72 3.13
13 17 48 2.82
25 5 11 2.20
28 2 4 2.00
So, you can easily see that the less shields you are buying the better deal you get. If you buy from 1 to 4 shields you are paying the lowest possible rate - 2 coins per shield. So, for example you are building a settler (cost 40) and you have 26 shields in the city screen and your current city production is 2 shields per turn. Instead of buying a settler, switch to a diplomat (cost 30), buy it for 8 coins, switch back to a settler, and now you have 30 shields in the city screen. Next turn you will have 30+2=32, and then you'll build a settler in a few turns.
Let's have a look at other options.
Option 2 : buy it - it would cost you (as per my estimation) 39 coins and you would get a settler next turn.
Option 3 : just build it - seven turns, no money spent.
Option 4 : build it till it is cheap to buy it (i.e. till you have 36 shields in the city screen) , three turns and 8 coins.
So let's see what we have (1st column - how many turns it took to build a settler, 2nd - how much money spent) :
Option 1 : 5/8
Option 2 : 1/39
Option 3 : 7/0
Option 4 : 7/8
so, you can see that you can get a settler two turns earlier than via its normal production. And it is for a very reasonable price of 8 coins. Option 2 and especially option 4 is just a waste of money. Moreover if you do a switch-buy-switch back thing three times during production of the settler (when you have 16 coins in the city screen switch to a phalanx buy it and switch back to a settler, and before, when you have 6 - use a militia), you would save 6 turns. If you build 5 settlers this way, your total gain is 30 turns. Awesome.
All I said before was applicable to both Civilization 1 and 2. Now, something that can be done in Civilization 1 only. As you are not loosing shields when you switch between production of city improvements and military units you can buy units really cheap. Let's say you have 2 shields in the city screen, switch from the settler to a city improvement of the same price - a barracks or a temple. Buy it. It would cost you 72 coins, then switch back to your settler or e.g. chariot (I would also suggest moving people off the shield producing squares to food or trade arrow producing ones for this turn to minimize loss of produced shields). You'll get a unit next turn. If you bought it as a unit, you would have spent 152 coins (it is just my estimation - check it in the game but should be pretty close). So, the first option would save you 80 coins. Awesome.
Another use of this approach is to rush build caravans and then help to build wonders. Briefly : set a Caravan in production, wait one turn, switch to temple or barracks, buy it, switch back to a Caravan, your city have to produce 10 shields to complete it. If your city production is 5 shields, it would take 3 turns and 70 coins to build a Caravan. Normal production would take 10 turns. You bought 35 shields for 70 coins, if you did it for the wonder, you would spent 140 coins. In other words, you saved 70 coins per caravan, or from 420 to 840 coins per a wonder. Awesome.
The only drawback of the latest approach is that to be able to do it, you should have a temple or barracks still to be built. For settlers and wonders it works fine (normally you build those units in cities without barracks). Veteran units unfortunately can't produced this way (I build temples in each city so it's not an option for me) as you already should have barracks there. Anyway you can do iterations using cheaper units as I described in the first half of my post.