As you have the New Classic Box, I think all you *really* need is the
Compendium pdf to have the 'full' version of the game.
Use the
Combat Garage to build designs; you have the counters you need in the Classic set already. Note that the die-cut counters in the Classic Box are better than any previous edition of Car Wars - back in the olden days you had full color cardstock pages that you had to cut out with your own pair of scissors. Now you might as well leverage your fancy printer to print out cars you want - the Car Counter Expansion set pdfs are great for that.
Much of this, and every thing else is 'bonus' material, Road Sections or Arenas to play your battles on or more counters. While the hard prints in vintage Deluxe boxes are pretty cool, mostly you just print your own now days - look at the pdfs available and decide what looks fun to you.
I really think with Classic, all you're missing are the in-depth design rules and additional vehicle types and weapons - and the Compendium pdf catches you up with all of that. While you're looking around at possibilities, the Arenas box gives you way more play surfaces than any Deluxe ever had.
Convoy is a fun solo choose-your-own adventure that you might like...