Joe Bob, you're going to have some extreme difficulty with trying to find a gun for under $100. Look at Spyders, JT Excellerators, Piranhas, Tippmanns, that's about all you'll find near that price range. And I'll take up the physics thing, all guns shoot the same distance provided their shooting at the same velocity, which leaves your accuracy to shot to shot consistency. There are a bazillion factors which will affect where exactly your balls end up, so basically all you can do is get good paint, get a good paint to barrel match, and get a good compressed air system for your gun. At $100 you'll be looking at blowback-style guns which have a small kick, therefore giving you a less stable shooting platform, which in turn gives you an even more erratic pattern. Blabbity-blah, these are little things, and are things that you'll just sort of notice along the way, get something reliable, put a good barrel on it, and get comfortable with it, that's my advice.
Best wishes.