Nope, a painter taught me to leave the roller in the paint can for use next time, also uses the small rollers for less spray coming off the roller as you roll.
That's not a bad idea, though 12" rollers would need a 5 gallon pail to fit into and I don't know how you deal with 18" rollers. Yes, short nap is better if your surface is smooth. Long nap rollers get messy, but on deeply textured surfaces you don't have a choice.
I see all these comments about oil based paint. I use oil based from time to time and have dedicated oil brushes (brushes for "all paints" are too soft for oil IMHO which needs a natural bristle), but have never rolled it in bulk (I'll use a foam roller with Rustoleum on my patio furniture). Brush cleaning oil in mineral spirits is indeed very easy.
As for water based paint, I have no trouble cleaning my good brushes with warm water and Dawn, but I must be in the minority, because I've had terrible luck cleaning rollers. And I don't use **** rollers either. On plain sheetrock walls, I use Purdy White Dove. On my stucco textured interior plaster walls, I use Purdy Golden Eagle. It's just that no matter how much soap, water and energy I put into cleaning my rollers, I find they're always stained by the tint of the previous paint. That's fine if it was white, or if I'm re-using it on primer, but unacceptable if that tint can possibly transfer to my finish coat. For the cost of a roller (which is well under the cost of the paint), I'm not risking it.
I do extend the life of rollers though. I'll cover them in a plastic bag between sessions (even for a lunch break) to keep it from drying out. Double bagged, it's safe for about a week.
But I do agree with the lint comments. A fresh dry roller (or brush) from the package is not ready to use. It needs to be washed and spun dry. That removes any lint from rollers, and gets the deepest sections of a brush wet with water, so that they don't soak paint all the way up to the ferrule and get crusty inside.