The main limitations you are facing are land, food and happiness. A good layout is one that allows you to put all good land to use and have the amount of specialisation that benefits your play style (Infrastructure junkies will want a good mix and specialise only when it becomes a no-brainer - like in a super-science city with Oxford and an Academy. People who are more concerned with immediate gains will want heavy specialisation everywhere, accepting inferior multipliers for incidental yields).
Flood Plains often give you enough excess food to support specialists (possibly to be whipped away - this is generally better if your only alternative is to work desert hills) or hammer tiles while directly lowering your health cap. Farming them is likely to send you directly into trouble with your growth caps. Workshops can turn them into some of the most powerful production cities possible in the early game (food-neutral 3-

tiles). However, unless the clump of flood plains is so large you couldn't work them all otherwise (growth caps) or you have very few workable hills, cottaging at least some of them is preferred.
Grassland can do pretty much anything - cottage it, farm it, workshop some if needed... it's hard to let a grassland-rich city go to waste unless your placement is off.
If you farm them and support specialists rather than cottaging them or work 1 farm per workshop, you are going to have 3 citizens per tile worked rather than 2. Trouble with growth caps or use of slavery (more efficient in smaller cities) suggests a tighter city placement for an all-farm layout.
Plains shine or suck depending on whether you have external food sources available. If you have to rely on non-resource farms to support them, all the tile does for you is give you an additional hammer (before Biology). Not worth it if you are in any way limited by health or happiness.
However, if you have plenty of spare food floating around, plains can be very useful... just 1 fish would allow one to work 6 plains cottages for a moderately powerful and balanced city.
I often find it most efficient to settle the grassland areas first, grow them to their cap and then divert the food resources to the second generation of cities to work the plains tiles as well. this reflects that generally 1

is worth more than 1

and therefore working grassland tiles is a higher priority without wasting perfectly useful land.
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Hills are boring because they're good for little other than production. Windmills are a good choice in food-poor areas where we couldn't work all hills otherwise and near rivers for Financial civs but mines will usually remain the norm.
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Not all resource-specific improvements are worth building. Silk, Fur and Elephants stand out for having yields so poor that a cottage/farm is often better if we already have the resource and don't want to trade them away to a rival.
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Something to also consider is overlap. While this won't be very common, a tile can be in the fat cross of 4 cities at once (if there is one 2 tiles in each cardinal direction). If that tile is a flood plain, each of these will take -0.4

which can make an otherwise great tile horrible. The same in reverse applies to forests and especially to forest preseves. +1

+0.5

in 4 cities can be worth more than another tile to cottage.
*****
I'd say that your chosen economy style becomes more pronounced towards the endgame. Boosted by everything there is to them, we have...
Towns for 1

7

Workshops for 4

Watermills for 1

2

2

Windmills for 1

1

4
All of these are awesome (the workshops slightly less so but I'd say the others are about equal). But even plain old boring farms can compete if they are supporting fully pimped-out priests for 2

1

3

2

. possibly to be whipped away periodically under the Kremlin or drafted 3 times a turn throughout your empire.
The problem is we can't have all this awesomeness at the same time because of conflicting civics.
There are a few reasons why wer're hearing more about awesome late-game cottage economies than other types:
First, cottages can be built on quite a lot of tiles - flatlands and grassland hills. If we're bending over backwards to make one improvement excellent we want it on almost every elegible tile.
Second, they allow either Free Market for efficient corporations (BTS only; high initial investment but with potentially ridiculous returns) or State Property (a sizable economic boost that doesn't require playing with yourself when you could push for something else).
Third, it's a smooth progression. You can start cottaging almost from the beginning of the game, and despite needing to mature they reach their point of utter awesomeness quite quickly. Farms and specialists suck after Great People generation ceases to matter much and before Biology enters the picture. When it finally does, the surge in food comes at a time when health is a big problem, making additional food less good than it could be.