As for modelling/animation I believe the best package to use would be Blender, because it's very easy to learn, has MANY different functions, can import/export to loads of different formats as well, and the rendering is just as good as the pro packages like 3ds and maya. Best of all it's free!
I used to use Maya 7.0 which was the greatest thing ever at the time, until it came to exporting your models into usable formats. Therefore I'd recommend Blender.
http://www.blender.org/
On the programming side I'd learn to use the SEARCH BOX at the bottom of the page here on the forums which is one of your best friends whilst you're using/learning/developing with Dark Basic or other TGC products.
You're also going to want to check out the awesome tutorials thread by Zotoaster which is stickied at the top of the DBPro Newcomers section of the forum. Inside that thread is also a tutorial on Simple Vehicle Physics, although I think you should have a look at some of the more basic tutorials first. Once you start to get a hold of arrays, functions, types and you get used to working with DBPro you'll be ready to get into the nitty-gritty stuff like creating an actual game/concept.
Tutorials Thread
DBPro Basics
Simple Vehicle Physics Tutorial
What I'd suggest rather than head straight into making a 3D racer is to design and program a simple 2D racing game to get the hang of the basics of handling vehicles in a game, albeit on 2 axis instead of 3 so it's easier, and you can work your way towards 3D from there.
Hope that helps.
