That depends on SP vs MP play. From what i've seen (nothing recently admittedly), the AI does not handle advanced start very well; hopefully that has (or will) changed. If you want a 'balanced' game (ie, don't want to get a huge advantage), don't buy techs, only cities/settlers/units; from what I'd seen earlier, the AI does not buy techs. If that's changed then ignore this.
In 'fair' SP (where the AI actually buys techs), buy a lot of 'base' cities (don't significantly spend on buildings, those are easy to produce), buy one culture expansion, increase pop only in cities where you don't have much food, buy a couple of workers instead of buying plot improvements except possibly a food improvement or two, and then buy techs. Your main goal would be to expand quickly land-wise (as it always is in SP...) so do that via cities. Then buy enough units to ensure you won't be killed on turn 10 by the AI, if you're close to one.
In MP, buy techs up to the next significant military tech, if reasonably possible; then buy a city or two, and then a bunch of units. IIRC there is a 10 turn peace to start the game, but after that it's fair game - and if you have more advanced units than anyone else, you will win (or at least not be slaughtered).