Do you cottage only riverside tiles or any grassland tile?
It depends. If the city is already explicitly for commerce, like a Bureau cap, then I will pretty much cottage anything, leaving enough food and production for growth/hammers.
I usually cottage the capital, settle close cities to work these tiles but I usually farm my other cities (and workshop them).
Bureau cottage cap is generally always good, if the initial cap has the appropriate land - it doesn't always. Moving the Palace is a possibility. On some maps, true Bureai caps can be hard to come by.
It is good to settle helper cities for the cap to keep cottages workings. Overlap is good anyways as you know, especially on higher levels. At least a couple of helper cities. Really depends on the land, although I've settled cities that would pretty much not be a great help later once the cap grows just to get those cottage rocking.
Outside the cap, generally food and production is key and is what you should be focusing on. one or two strong cottage sites is good though if the land is suited for that.
Workshops are very good later on. I usually plan for that out some point on the outward growth of cities plus techs/civics. (if they game comes to that point)
which leads to
I'm always concerned about not having enough commerce. Building research is fine but if I'm building research I'm not building other stuff.
what stuff?
You have experience now and know quite a few basics concepts and things that help you win on higher levels. However, some of your comments seem to denote a lack of focus or planning in how you play the game.
You seem stuck on cottages and research, but I'm not sure what your plan is. With the exception of Culture, which can be won most passively, most VCs require expansion, setting up economy, and warfare - whether you like it or not.
Generally a strong Bureau cap and GP farm, plus well designed cities can get you to a good point to do what you need to do on any level. I detect a lack of emphasis and use of great people which is a big part of playing on higher levels. Gold should be easy to come by (gpt from trades, tech trades for gold, conquest, etc.).
Ultimately your empire is setup such that bpt output is strong due to multipliers so that when you do get the gold you can max research. You can build Wealth in cities as needed when those cities have not much to do (get away from building useless stuff). Building research is generally only good early on to get to Currency fast or much later when you have gobs of gold to max out..like for Space.
Get to a strong military setup and then just pump out an army..whip whip whip..to get out units. Cities like the Cap stay large to keep research going, and HE to build units quick, but most other cities can be whipped hard and should be setup for that purpose when needed.
Again, you have this fixation on finding ways to "keep pace" with the AIs research wise on higher levels. The point is that on IMM+ the AIs are pretty much always going to out tech you early on due to their bonuses. However, AIs are pretty predictable in how they tech. So what you do is use that to your advantage to tech and bulb an appropriate path for your goals. trade techs for anything you missed of any importance, get a military advantage, whip, go kill peoples.
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you can go into settings and get rid of this