Since you live in California you should become familiar with our "Green/Red Sticker". Here is a link to the California DMV that gives the official version:
http://www.dmv.ca.gov/vr/ohvredgreen.htm
IN California, all off road vehicles are supposed to be registered in order to ride on any public lands. Private tracks are okay, but any BLM or forest serivice lands require it. In addition, bikes that are 2003 or newer that do not meet the EPA requirements are restricted from riding in most areas during the summer months.
You will obviously be buying used to get into your price range, and probably older than 2002 which means that the bike will be eligible for the desired "green" sticker.
As I said above, all off road vehicles are "supposed" to be registered but the truth is that you can often get away without the registration. The enforcement is very limited in the desert areas due to the numerous entry points. The forest service areas are another story.
When you go shopping for a bike you will find a lot of bikes that don't have California registration. Some of these will be because the bike was recently brought into California from out of state. Some will be because the owner rode tracks or desert and never bothered to get the proper registration. While it is certainly possible to get such a bike properly registered it will be a hassle, requiring several trips to DMV and one to the CHP. For that reason I would pay more for a bike that had the proper registration and pink slip.
As for the type of bike: You are thinking of jumps and track so I would definately go with a full MX bike. You are 21 and aggressive so I suspect you will want a powerful bike. You have street bike experience so you should have the basics down and will get the hang of dirt pretty quick.
I would normally discourage a beginner from buying a two stroke 250 but in your case it is what I would recommend. You should be able to pick up something like a Yamaha YZ-250 from the late '90s in your price range that would suit you well.
Be sure to budget the necessary safety gear: Helmet, goggles, boots and gloves are the essentials. A chest protector and knee pads are highly recommended. Unlike the street bike, you WILL crash on the dirt bike. Get the protective gear before you get hurt.
Rod