Theres serveral really good brands of oval/offset chassis. Phantom is probably the most popular brand, but the setup/adjustments are so important on oval karts that the best brand for a new racer usualy comes down to the one that you can get the most support/help from either the manufacturer, your local kart shop or fellow racers.
If possible, I'd suggest you go out to the track and start watching some races to see who the winning drivers are in the various race classes. (write down their #'s/colors) You can then usualy pay a small aditional fee to enter the pit area and find where these drivers are pitted. Don't bother them when their frantically getting their karts ready for the next race, but when you find them kicking back you'll find
most racers will gladly give polite newbys all kinds of good advice including what brand/model their kart is.
Many top drivers seem to buy a new chassis every year or 2, so you may find a bargain on one of their used chassis thats a proven winner and already setup/adjusted for that particular track. (this seller would probably also be more inclined to help you out with all kinds of other issues you'll run into on down the road)
On a tight budget, I'd try to find a used kart somewhere in the 2005 range. This age seems to be old enough where the value has dropped a bunch but still new enough to be competitive. Around here, I've seen serveral top brands this age selling for around the $700 range (no motor)
Heres the best dirt oval race forum on the net:
http://karting.4cycle.com/forumdisplay.php?f=81
I'd suggest you spend some time looking around, (search the term
volusia, and then post this same question in that forums
General Discussion section. I'd title your thread
Volusia rookie seeking chassis brand advice You'll probably get replies from racers at your track.
Here's your tracks site:
http://www.volusiaspeedwaypark.net/
Good luck man, you've got a steep learning curve ahead but dirt oval racing is a blast and well worth all the effort!