Keeping your price range in mind, I would say either a good KTM200 or 250 EXC...they have wide ratio tranny for dez work w/ very usable/learner friendly power but also lets yo go fast as you get more seat time. Suspension and handling on the EXC lineup, both 2T and 4T, really is tough to beat for a box-stock off-road bike
The 00-02 400EXC's can be found in that price range also and are excellent bikes w/ broad appeal (tight trail and dez also). The KTM four strokes hold up well also.
Another bike that does excellent in the off-road world and sells a little cheaper due to shaky re-sale is the GasGas. Nice bike, handles excellent and in a few years will be considered as norm as KTM. As for right now, you can buy them pretty cheaply.
The WR250Fis another possiblity for a lighter, easy to ride four stroke, and it seems to be pretty durable.
The KDX's are nice machines, although I think there are better choices for dez...again its not a bad choice by any means, although the KTM's and the WR will allow you to get more aggressive as you get better.
About the only bike I would shy away from is a box stock MXer, too much $$$ and effort to trail ride. It can be done (I've done it for years), but in the end the race/trail bikes available now are dollar for dollar hard to match.
W/ any of these bikes, making sure it is properly maintained is paramount.