Try to find something a step up from the bottom tier jump king/walmart 15' round tramps. They'll be okay for height, but won't have a very sturdy frame and most of them won't have UV-proof spring protectors (which will rot in the sun super fast.)
As far as bounce goes, I have a 15' aero bounce (retail ~ $900, so a modest step above a wall mart tramp,) and don't have any problems getting enough air for any kind of single flip, but doubles are pretty much out of the question. I'd say it's enough to tweak a grab, but not enough to hold it for any serious length of time.
Also, a net isn't really necessary unless you want to learn inversions of any sort. I don't find I have any trouble controlling bounces well enough to stay on the tramp with any sort of straight bounce or spin, but all bets are off when you're learning backflips. I bailed off mine and chipped a bone once, and that was enough for me to go out and buy a net.