BobA has hit the nail on the head: if you're going with a compressor-based HVLP gun, you need to look at the gun's air requirements and then size your compressor accordingly. Be prepared for sticker shock: most HVLP guns want a lot of air! You're probably talking a 20-25 gallon tank minimum, along with a compressor that can keep it filled. You could buy a smaller compressor, but it will run continuously which isn't a good thing. And you definitely don't want to run out of air in the middle of spraying! If you do decide to go this route, I'd suggest getting an oil-lubricated compressor. My oil-free pancake compressor makes more noise that just about any other tool I own!
The other alternative is to buy a better turbine-based HVLP system. The Wagner you were using is probably a 2-stage turbine. A 3- or 4-stage turbine will provide better atomization, though it may still have problems with some finishes. In theory, a 4-stage system is supposed to be better than a 3-stage system, but a recent Fine Woodworking test claimed that they didn't see much difference in finish quality between 3- and 4-stage units from Apollo and Turbinaire (two of the better turbine manufacturers) when spraying water-based clear coats. YMMV.
Unfortunately, if you want a good setup you'll probably have to spend $700+ for either type of system.