Well, the first thing you need is a good, sturdy trowel, preferably one with a wooden handle (easier on the hands and lasts longer than plastic). Then you need a cultivator for your in-ground plants. Our three tine cultivator gets a good work-out frequently. You also need a hoe for rough-chopping weeds. A decent shovel, either a spade or a pointed shovel--you'll eventually end up with both, but choose the one that meets your immediate needs.
The best advice I can offer is--buy the best you can afford. Two cheap trowels at $1.99 that bend or break isn't as good as one strong steel trowel with a wood handle at $5.99. If you are on a tight budget (and aren't we all!) go to auctions and see what old tools you can pick up at bargain prices.
Keep the tools sharp (shovel, hoe, and trowel) and clean. I oil ours frequently since we are in a very humid area and things can rust overnight!
You have the right approach to gardening--get what you need and see how it works for you. You'll be a great gardener!