Tile Improvements and Terra-forming
Before anything specific about which tile improvements you should use, its important to know when to place tile imps in which cities. Here is an explanation how CtP2 cities collect resources:

In CtP2 all cities work the tile of the city itself all the time. However, in a small city (size < 7), the city radius is only 1 tile large instead of 2 while each and every tile in this radius is being worked. A size 1 city collects 1/6 of all resources on these 8 tiles, a size 4 city 4/6 and a city 6 city works all the tiles 100% (6/6 of all resources). Once a city reaches size 7 the city radius grows larger and the second ring of tiles can be worked. Now this may seem illogical at first but the first 6 Pop will keep working the first ring at 100% efficiency while the second ring gets worked by the 7th Pop at 1/12 efficiency (the next radius growth will take place at size 18, 18 - 6 = 12, so 1/12 of all resources in this ring is collected). So in a size 12 city, the first 6 Pop will work all tiles in the inner ring at 100% efficiency while the next 6 Pop will work the outer ring at 50% efficiency (6/12th of all resources).
Full thread here.

So that pretty much means build tile improvements around your biggest cities first, and from the inner ring outwards.
However sometimes the game isn't as simple as that...
As described a city collects resources at a fraction depending on the city size, so when is the 'threshold' when a city definitely doesn't need tile improvements, and when it definitely does? The answer is, there is no simple answer. It depends on your position in the game and the amount of time you anticipate you'll have to generate Public Works before you get attacked (or you want to attack).
Remember that smaller cities grow faster than large cities, so it might be wiser to build tile improvements on the inner ring of a small city that's growing fast, rather than on the outer ring of a large city that has slow growth. Even if this is currently less efficient.
Food Tile Improvements
Every city should have some food improvements, so the city can continue to grow as you improve other areas. A city with too many farms can effectively use specialists such as scientists and labourers to compensate for the lack of commerce or production tile improvements there.

Production Tile Improvements
There is not much to be said here, just stick to building mines on hills or mountains, and not grassland or plains. More production = more public works = more tile imps. More about this in the comparison table below.

Commerce Tile Improvements
In some positions commerce tile imps can win you a game, in others they will waste your public works. The two resources split from commerce are gold and science. Commerce will be split depending on your science tax. A greater science tax obviously leaving less gold in the bank.

If you intend to build lots of commerce tile improvements this has to be part of your overall strategy, one which includes rush-buying lots of things (because of all the extra gold you get) and keeping your wages as low as possible all the time, so the cost of wages take as little as possible from your collected commerce.

This strategy works well with low production/high growth terrain such as grassland. Where city sizes will generally be larger, so you'll generate more commerce. Communism is suited to this with both higher commerce (but not science) collected and higher production than Democracy.


Roads/Railroads
Build roads before Knights, then railroads before Tanks. Roads can also move settlers out faster to good city sites, if you need them quickly before a government change, just don't forget to guard the settlers.

Terra-forming
Common terra-forming strategies include grassland to plains and forest to plains. If you choose not to terraform grassland to plains, you'll probably need production elsewhere, whether from labourer specialists, or a commerce rush-buy strategy mentioned above.

Grassland cities will obviously grow faster in the beginning and provide more natural commerce because the cities are bigger, but they will not produce enough production.

Plains cities will provide good natural production to build lots of public works and thus farms fast. There is really no downside to plains.
Here is a comparison of tile improvements value for cost.
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