Tom,
I've play raced, trail rode, enduro'ed, improved, modified and generally mucked about with the DT360's (in the day). I've had great fun riding and modding the thing, and I have affection for the 'old nail'.
But my best advice is, if you want to race, get a race bike.
Even with dollars it will take time and expertise to get a bike that is fun to ride let alone competitive.
Guesimates; chamber $200-400, Tyres $200, gearing $60, front suspension $200, rear suspension $400, and more.
$500 is a good price for a complete running DT360. You would be better off grabbing it, using it on the road and/or trail and maybe restoring it (now or in the future). Alternatively, talk the price down and put the DT on to Evilbay. If it is complete and presentable you might fluke $1000-1500 and you'll have money enough to buy a good dedicated VMXer.
Talk nicely to some of these old 'would be could be's' and they might give you more specific advice and help in choosing a bike.