I shot my underside with a $10 Harbor Freight HVLP gun. But I had it off the frame and flipped. I usually use a Techna Pro HVLP or an old school Devilbiss suction but I was shooting KBS epoxy mixed with ceramic microspheres and that stuff is very hard to get off the gun so I just planned to toss it when I was done. It was worth $10 to not have to clean and believe it or not, it shoots pretty well. Almost shockingly well. The gun is the same as he linked to, but I used gravity feed instead of a pot. For the underside, if you're not painting a color, just the epoxy, the gun finish really isn't super critical. You'll have way more issues with temperature, humidity, and other variables. And if you're doing it on the frame, you can't get long controlled sweeps anyway. So you probably don't want something that's laying down a lot of paint because you can't move as fast when you're working around things. With an HVLP you'll be putting down plenty of paint so the nooks and crannies are fine. With a beginner using a normal gun, he'll probably move slow with a lot of off and on the trigger anyway so he can adjust his timing or go over it a few times while he's in the area. Either gun will work fine. He'll get more "overspray" with the normal gun, but it's not $2000/gal paint where you're worried about losing a bunch to overspray. But he can use the HVLP and just adjust his speed, or volume, so he's not getting drips.
I shot the rear wheel wells when it was still upright. It was a little difficult around the rear inner wheel well, between the door post and wheel well, and the tail light and wheel well, especially at the top. You have to shoot blind and just reach your hand up there. But don't forget I was using a gravity feed gun so I had a cup on top. His pot gun has a lot more room. I turned down the paint volume because I knew I couldn't move fast and didn't have a lot of room. Then I went up with a light and mirror to check. Don't spray too long or too short. You'll be able to get it all. And up there it doesn't have to look pretty, just get covered. No one can see up there.
Mind you, I'm not a pro, but I have shot about 12 cars and only messed up one. If there's any pros here, pipe up.