LED bulbs comwein many colors from very cool almost blue to very warm with what I think is a horrible yellow cast like old incandescent bulbs. Yes you can get 3 or 4” cans no problem I like LEDs in the 4000K range it mimics bright sunlight and makes colors stay true at night without that yellow glow to everything that changes all the colors you tried so hard to make work.

You can actually get GU10 or MR16 fixtures and just change the bulbs with retro fit LEDs we have done it all through our house where we had all halogen MR16s I do think the idea of checking out the different K values is good.

Yes absolutely true. I should have been clear that you have more options when you buy a true can with a bulb versus a faux can that has an integrated bulb (faux cans are really useful but once you have them all installed in your house they are yours!)

" I apparently like 'a horrible yellow cast' as I like 2700K lights, I use 3000K in my office and my husband has 4000K in his painting studio." LOL! Apparently I also like that horrible yellow cast. And no, it's not yellow to me, just warm. Not all space-ship-y ; - )

We used these remodel cans, the link is for 5" which I preferred since we used 2700K. They have them in the 4" size as well.

IC20R 5" Remodel Can

Juno Lighting IC20R 120V 5 Inch Remodel Dimmable Incandescent Recessed Downlight · More Info

And this trim, though again, you have other options for color and style:

Juno Lighting 204W-WH Gloss White Cone Trim(well the pic for the can trim isn't showing up). Ah, there we go : )

Juno Lighting 204W-WH 5 Inch Gloss White Baffle With White Trim Ring Recessed Li · More Info

Just helped my Dad install some retrofit LED recessed light. The ones he found at Home Depot have a switch inside that allows you to select the light/color. The choices were 2700, 3000, 3500, 4000 & 5000, adjusted with a slide switch right on the top of the fixture. Wish they had that when we replaced ours a few years back. Having the ability to adjust them differently for different rooms or adjust them as your needs/wants change is genius, and much less wasteful for the environment.

It was something like this one:
https://www.homedepot.com/p/Halo-RL-5-in-and-6-in-White-Integrated-LED-Recessed-Ceiling-Light-Trim-at-Selectable-CCT-2700K-5000K-665-Lumens-RL56069S1EWHR/304533541