Painting the interior, and eventually exterior, of the house.

Brush and roller is too slow.  Former owners used loud colors and I am needing numerous coats of primer to get the new stuff to look good.

Never used a pro paint sprayer before, only small airbrushes for gun refinishing etc.  

Youtube videos show a ton of atomization of the paint/overspray.  So I guess I need to decide if I spend my time brushing and rolling or spend my time sealing every damn square inch of the room I don't want to get atomized paint on.

What am I missing?  Are all paint sprayers the same?  Will and spray paint with minimal overspray and atomization?

Thanks.

As you've already found out, you need to lay down drop cloths and mask everything.
You might also need a hand mask, which can be a large piece of cardboard, to protect certain areas .
And on top of that, you'll need a wide roller to smooth out the paint after it's been sprayed.
Renting the unit is another cost.
I've done spraying and rolling, and it is simpler to just use 5 gallon buckets, and a roller.
Get two people, one to cut in and the other to roll the paint on.
When the cut in person gets far enough ahead, they can move to the second roller.
If you're not a pro, spraying can take longer.

Cover everything you don't want to get paint on.  The atomized paint will leave dust over everything.

Wear a properly fitting mask of the appropriate type for filter particles and eye protection.  Good ventilation in the room is a plus.

I used one recently to paint the walls in our unfinished basement, which had been painted green by previous owners.  It went fairly quickly after I got the hang of it.  I used a piece of cardboard to shield areas from overspray.  After doing it, it was fine for my unfinished basement, but I wouldn't want to do it upstairs in our main living area.  Having to mask off all the trim, doors, windows, and to cover all the floors and furniture would be a major pain, and I don't think it would be worth it.

You don't want to use a sprayer in that situation.  They are pretty messy unless you tape up everything.  Might as well just do numerous coats.  For houses that are getting gutted, it is one of the best tools i have ever bought.

What paint and primer are you using? I've never had a problem covering old paint using Kilz 2 and good quality paint. One coat of primer and 2 coats of paint and it's done. I've covered hot pink, black, and disgusting sea foam green. All came out great.

GRACO airless - buy!

I have a graco x5 that I use when nothing is around that needs to be covered. If anything needs covering I roll. The key to covering loud colors is a good primer. Kilz 3 and zinsser bullseye are good. I prefer the kilz 3 as I think it has less of a smell. Only once or twice have I had to use more than one coat of either of those primers to cover something enough for paint.

As always, get both.

Buy a GracoX5 and the pressure roller attachment.

Cut in along the baseboard, ceiling, and trim with a brush. Power roll the rest. Do as much area as possible at one time as the X5 clean up isn't worth using it for small areas.

If you have skill, spray.

Since you are in DIY, I bet you can get the quality you want with the speed with a bit of practice. Prep is probably around half the work, as it is with most things.

I have only used a Fuji HVLP, never an airless. Different animals for different tasks.