Should I immediately clean the paint sprayer after use

I have used a sprayer to paint my house before we moved in. While I can't qualify how much more paint I used, it did feel like I used more compared to rolling, but I think part of that is because it goes so quick and I may have been painting over the same areas more than I would have with a roller.

One thing to note though, when I sprayed my home, there was nothing in it. No flooring, window treatments, etc. Spraying, no matter how careful, will leave some atomized paint in the air, which will eventually hit the floor or whatever else you don't want to have paint on it. Be prepared to mask, tape, and tarp everything you don't want painted that can't be removed from the room. You will want a mask and a respirator of some kind (you probably don't need anything fancy). The mask I used had a roll of film built in it so that I could get a "clean view" when too much paint got on it. That was especially handy when doing the ceilings.

Personally, now that I have moved in, I would roll instead of spray.

Getting a smooth finish without purchasing an expensive HVLP sprayer is fairly easy. Start with any good grade paint, and treat it with Flotrol acrylic additive at a rate of about 1/2 pint per gallon and mix well. If you get a real thick paint, you can increase the amount of Flowtrol up to one pint per gallon max. I use and recommend Purdy brushes. For trim, I like a sash brush, (angled style). Be sure to pick out a brush for latex paint, usually a combo of nylon and poly bristles. The ends of the bristles need to be very tapered and soft. Check out the Purdy ExtraGlides for latex.

Your technique is important also. Always try to finish with long smooth strokes only using the very tips of the bristles. Properly treated paint and the right brush used well will give you fantastic results. Good luck.