I have a dedicated HVLP gun with it's own turbine compressor. It shoots latex fine, you just have to thin it to the correct consistency for the needle you are using. There is a viscosity gauging device that came with the gun, but after using it once or twice, you get a good feel for how the consistency of the paint needs to be to work. I just thin with water and stir it in well. I try it, and if it's still too thick, thin it a bit again. Most times I just thin it directly in the quart pot of the gun, unless I'm going to be shooting a lot of surface and expect to use an entire gallon.
I love how the HVLP is very controllable to eliminate runs, but has great coverage and almost no overspray. The only thing is that the paint has to be lump free. Lumps really screw up the operation. I strain all the paint before using it if it's older paint.
I use semi-gloss paint myself, as it's easier to clean marks off of later. If you adjust the application rate down to fairly light, the paint dries quite a bit in the air blast on the way from the tip to the painted surface. You can adjust it down so that you get a matte finish even with gloss materials. Or, up the application rate, and it will "skin" and give you a gloss finish. I can also change the directionality of the spray pattern, from a round pattern, to a angled composite pattern, to a vertical or horizontal fan. Each of those patterns will give different finish characteristics. That is one of the things I really like about HVLP. I shoot a lot of stains and varethane with mine, and I can make varethane look like a hand rubbed, matte oil finish just by adjusting the spray distance and application rate.
Set up a trial piece, and adjust how you shoot on the paint, until you get it to look like you want. HVLP is one of the easiest guns to get good at using, if you pay attention to how the paint is going onto the surface, and adjust your speed and distance away to get the look you want.