I've been reading through and admire your enthusiasm and earnestness to shall we say, cannonball into the deep end of the pool.
If I was starting with a blank check, but to keep things reasonably economical, here's how I'd go about it. This is from doing this play with cars thing for 25+ years starting when I was in my early 20's:
* Truck - if DD'ing, and these days they are pretty plush, a heavy 1/2 ton or 3/4 ton extended or crew cab, depending on how much of a back seat is needed. As new as possible, with the most powerful gas engine and shortest gears avaiable. If only towing, buy used. Look for an 04-06 3/4 ton from any of the Big 3. $10-12k should net you a decent truck that will last in this role a good many years.
* Trailer - Reasonably sized enclosed is the way to go. I have a 20' with front cabinets for an 18' floor length and it works fine, but then I race a CRX and a Civic; OAL of 12.5'. I see no reason to go more than 24'. The trailer can double as a garage bay for the race car, and also as said, sleeping quarters at the track.
* Race Car - We are all obviously partial to IT cars here. And there are lots of deals to be had given the economy. To get your feet wet and your water wings under you, I would buy something that is cheap, reliable and easy to work on. Two years ago I bought an ITB '87 CRX for $4500 with a pile of spares. It has gotten both me and my son licensed, only having one real mechanical failure (tranny) where I got to learn how to rebuild one from stealing the bustificated part from the spare that came with the car. Other than that, it was only been normal race car maintenance (brakes/bearings/hubs) and a couple of small things, over 16 race weekends the past two years. Honestly, I'd look for a deal like that. Once you are settled into a race routine, then a decision can be made to start making improvements to the car, or to buy something bigger/faster/blingier.
* Tools and Parts - At the track I have the basic repair parts: brakes, spare hubs, radius arms, tie rod ends, plugs, cap, rotor, axles, and spare wheels and tires. All carried around in a bunch of plastic tubs. Occassionally I do bring a spare tranny with me. The most I've ever done at the track are hubs and brakes. And those hub changes usually end up getting done 15 minutes before needing to be in false grid.....Tool wise, Sears sells a great 250 piece set all nested in it's own toolbox. Best thing I ever bought. I also carry small and large floor jacks, a couple of breaker bars, a cheater pipe for when 1000 ft-lbs of torque is needed to bust a nut loose, and an assortment of various glues, epoxies, gasket goop and sealers. Example: at Watkins Glen last October, I discovered a small CV joint boot tear. Rather then swap the axle, a friendly competitor suggested to get some grease in there, clean it up and super glue it. Did the arts and crafts project at the start of beer time Saturday night, and the fix held all through the 45 minute race the next day, as well as a full double-dip 8 session race weekend 3 weeks later that the kid and I ran. Mr. Murphy's laws and order will always leave you without the exact thing needed to fix a problem, but people you have never met before will jump in to help, usually with exactly what is required.