Lotsa great advice so far, so I'll just share my growth as a home brewer. Shortly after I started (with a bucket and an extract/steeping kit), I went BIAB partial mash and all grain, and around the same time I scored a cheap fridge and some kegs. Shortly after that I got a burner and kettle large enough to do full boils on 5 gal batches along with a grain mill so I could control my crush and keep more uncrushed grain on hand. I've since added a 10 gal cooler mashtun and a 10 gal cooler (soon to be electric) HLT. Where I'm going is that the hobby will grow with you, as will your collection of goodies.
I'd first stress trying all grain, and for that BIAB is awesome. You can mash about 10 pounds of grain in a 5 gal paint strainer from HD or Lowes, or you cna order (or make) larger bags. I know Midwest has 'em that'll easily line a 10 gal beverage cooler and hold 20+ lbs of malt. Second, if you have a chest freezer, why not get an inexpensive temp controller and use it as a fermentation chamber as others mentioned. Controlling fermentation temps will drastically improve your beer, extract or AG. Kegging's great, don't get me wrong, I only bottle beers that I plan to age long term anymore, but it's secondary to making great beer. Get the kegging setup when the budget allows. Spend money on brewing books and brewing magazine subscriptions. Anything you want to know about the craft is in books, mags and online for you to read.