Grasslands and plains can be used for a few things so they're flexible, you can also get food from city states which can make an otherwise poor city grow well. Remember that science is determined mostly by city size and specialists so a science city needs a good amount of food. Gold works best on coastal cities, especially with 2+ fish/pearls, or cities with several luxury resources nearby. Rivers can work for either gold or science and you can get cities that are good for both. Production cities just need hills (or forests) and enough food to support the mine workers, they also benefit from having resources nearby but that's not critical.
Some building & improvement combinations are really good too. A riverside jungle with a trading post near a city with a university can reach +4 science with the right social policy (technically +6 with the 50% bonus form the university). That same tile will give you +3 gold but if you add in a market and bank it will need to be a pretty large city to be able to support an extra three specialists while still working those tiles. The market and bank have no maintenance though so building them in a bunch of cities won't hurt as much as it does with other buildings.
One thing to keep in mind is that to really get the most out of the city you need to be using specialists. But, if you're not hurting for cash like the OP you can get away with a few extra buildings. A library will give you a few extra beakers in any decent sized city so paying 1 gold for 3-5 beakers may be worth it. The problem there is that the AI governor likes to work science specialists so you may end up losing tile workers if you're not micro managing the city.
So, considering all that I would say 'focus' each city on something but don't worry about making them exclusively science, gold or production cities to the extreme that you would in Civ 4. Just be mindful of the building maintenance and even if you don't micro-manage your cities consider at least checking the box for manual specialist assignment.
Some building & improvement combinations are really good too. A riverside jungle with a trading post near a city with a university can reach +4 science with the right social policy (technically +6 with the 50% bonus form the university). That same tile will give you +3 gold but if you add in a market and bank it will need to be a pretty large city to be able to support an extra three specialists while still working those tiles. The market and bank have no maintenance though so building them in a bunch of cities won't hurt as much as it does with other buildings.
One thing to keep in mind is that to really get the most out of the city you need to be using specialists. But, if you're not hurting for cash like the OP you can get away with a few extra buildings. A library will give you a few extra beakers in any decent sized city so paying 1 gold for 3-5 beakers may be worth it. The problem there is that the AI governor likes to work science specialists so you may end up losing tile workers if you're not micro managing the city.
So, considering all that I would say 'focus' each city on something but don't worry about making them exclusively science, gold or production cities to the extreme that you would in Civ 4. Just be mindful of the building maintenance and even if you don't micro-manage your cities consider at least checking the box for manual specialist assignment.