Improvements is really out of date and just plain wrong.
Foreign Ministry should be second if you plan on doing tech deals.
Factories should be next if you're doing tech deals (which you should be) so you can quickly grow
Banks and Stadiums should be bought one after another. If your gross income is under $85, buy 5 stadiums and then 5 banks. If it's above $85, buy 5 banks then 5 stadiums.
etc
That's as far as I've gotten. As has been recommended before, join an alliance and you'll usually get good guides and experienced players to help you through it.