This is really in the vein of "advice to a young cook" more than principles per se, but here goes:
The most important piece of advice is very compatible with low quantities of money: cook! This is one of those things that is mostly learned through experience, so trial-and-error is likely to continue for some time. There will be times that it feels fruitless, but think of it this way: unless you screw up incredibly badly, at the end of the process you still get dinner.
Coupled with this is the second cheap piece of advice: taste everything you can before serving and consider the seasoning. The easiest way for most people to improve their cooking is just to taste and season better.
These two are good for other cuisines too ;-) Seriously, (interest) + (internet recipes) + (trial and error) = knowledge of other cuisines.
I found a basic recipe book like the joy of cooking incredibly valuable. The recipes aren't the greatest, but if you want to know how to do something new (carve a chicken, make a stew, etc.) the advice is usually pretty fantastic. J of C plus the internet have you pretty much covered if you're a little willing to improvise.
Equipment: you don't need a lot to get started. For a single person just starting out I'd get:
- 8" chef's knife plus plastic cutting board
- a medium-sized nonstick pot holding a gallon of water or so
- 12" nonstick skillet
- small roasting pan
- silicone spatula
- big honkin' wooden spoon
- measuring cups/spoons
- plastic strainer for pasta (also subs in as a strainer for other things)
- big metal or plastic bowl; maybe a few of these
This stuff gets me through 90% of day-to-day cooking. There's other stuff you may want at some point (nonstick and heavier pans would be high on my list), but most things can be cooked with just this.
Key cheapness advice: buy inexpensive meat and learn to cook it well. Tough and cheap cuts of beef or pork in braises or stews, roasted whole chickens, etc. It's more work than nonthreatening chicken breasts, but it's more broadening and better on the wallet.
Lastly, links. You probably don't need me to tell you about epicurious or anything, so I'll stick with two:
has transcripts of every episode of Good Eats, a basic and entertaining cooking TV show. The transcripts walk you through cooking a few things in extreme detail and are always useful when you're trying new stuff.
is an ongoing series of columns about food science for the home cook. Interesting, cheap, and a good source for fun and easy projects.