When I made the switch to Civ3 the learining curve was a bit high. You just have to play ALOT of games to get used to it. It took me about 12 games before I got the hang of it. Start at Cheiftain but don't stay there. You need to challenge yourself with the higher levels which all play just a little different from the next.
Don't give up. You just have to get over the hump. I think its better to learn on Tiny or Small world first. Games move much faster this way.
On the other hand if you start on a large world you may not come in contact with another civ until well into the Middle Ages. This may give you time to build your civ.
Some of the hard lessons I've learned are:
* You must have a supply of Iron ASAP. This is very important because if you don't you will not be able to build Swordsmen who are the best early attackers in early wars.
* Build the core of your civ ASAP = at least 6-8 cities ASAP.
* Two defenders per city ASAP.
* At least one worker per city for roads, etc.
* Get to Monarchy or Republic ASAP.
* Build Barrackd, Granary, Temple, Marketplace before Wonders.
* Don't build Aqueduct until City Size 5 or 6; you are just wasting money if you build early.
* Set Barbarians at Roaming and ransack their huts. There is gold in them there hills....
* Set play Prefs for both Warmonger and Peaceful game. This gives you the best chance of winning. There are actually four ways to victory in Civ 3: Cultural, Dipolmatic, Domination, and Histographic.
And the answers to your biggest problem: Resource and City Construction:
* You MUST watch your status screen EACH TURN.
* At the very start (Turn 1) set your Science slider to 70%. Keep an eye on it and as soon as your cash flow goes negative turn it down to 60% etc.
* Keep an eye on your cash flow each turn and always set your Science slider for maximum cash flow without going into the deep negative numbers.
* Leave the entertainment slider at 0% until the Industrial Age.
* Seek out resources and build a colony on them. Always protect them with a good defender. You MUST build a road to the Colony for it to be of use.