Yeah the number of units you need to build in Civ 4 is one of hte biggest changes to previous versions. If you come all the way from Civ 1, you will have an instinctive aversion to too many units. unit support was EXPENSIVE back then. You would have a maximim of 2 units per city pretty much until very late in the game. Now with a lot of free units, and non free units costing one gold a turn they are really really cheap.
If you want to see one way to play the early game go watch TMIT's REXing extravaganza as Suleman. The thread is here
http://forums.civfanatics.com/showthread.php?t=352249 this video diary is here
http://www.youtube.com/watch?v=1SoMQ9mtvYE&feature=PlayList&p=0CF210671DFB4C23&index=0&playnext=1
Upto about 1AD he builds pretty much nothing appart from warriors, settlers and workers. He does have quite a lot of gold specials to keep his economy afloat, but oyu can do something similar iwth a cottage city particularly if you are financial.
As an old school civ veteran myself I would suggest not playing random leaders, but go darius of the perisans. You have two solid financial traits in financial and org, which helps your economy out hugely. Plus immortals, the unique unit (replaces chariot) are great if you find yourself close to someone at the start and need to take them out early.
As every leader needs a slightly different strategy, so I would not play random when you start a level. Only play random when you are more comfortable with the difficulty level.
Ignore the starting wonders unless they are still in play late. I do normally make a play for the oracle, but don't worry about it too much.
The persians start with hunting and agriculture so something like Animal Husbandry, mining, bronze working to start with. Then if oyu have horses and want to rush someone get the wheel and pump immortals.
Librarys and marketplaces are much worse than previous versions of civ as the bonus is only 25% not 50%. This is balanced by the fact that they allow you to run specialists as well. So early game DON'T BUILD THEM unless you are going to run specialists in that city. That means that in the early game you have a max of 2 libraries in your 6 city empire, which again feels really weird for an old school civ player. Your capital can have a library, and if you have another city wiht good food specials then it can be a good place to build one too, to have 2 scientists.
Scientist specialists are great for firstly building an academy in your capital and secondly for using the "bulb" power to research the right techs to help you win the race to liberalism (which is pretty key at high levels). Note also that the techs now have really widely varying amounts of lightbulbs to learn, so be careful when taking a free tech either from libralism or the oracle. Nationhood is normally a good one from liberalism, for the oracle I normally get metal casing. Other people suggest asthetics if you want to go for the literature wonders. All these techs are good for trading with the AIs.
Diplomacy is the other key thing, it is quite different to previous versions. Religions are normally key to diplomacy. Be very careful when selecting state religion, that is why founding a religion is not so useful on high levels as you NEED to be the same religion as someone if oyu want peaceful relations. So you have to let them found it then spread it to you. Sometimes you can found one and spread it to them, but on higher levels that normally takes more resources than you can spare.
Civ 4 has got a lot of changes to the way things work compared ot the previous versions, and you have to unlearn some things. The tile improvements are a lot better than they used to be and there are lot more uses for population (whipping for production or using specialists). The bonus you get from a special tile with the correct improvement is huge, and you need to get those working for you fast. So you prioritise the techs that allow you to work the tiles. Calendar is more important than I thought it was too, I should get that earlier I think. The extra happy and health from calendar resources can give oyu a huge boost.
Anyway I think that is enough for one post

. I guess I should try to write a guide for people who have some false tactics from previous CIVs (not that I played CIV3 much). I played huge amounts of Civ 1 though.