This. Your pack has to fit and carry well, and your sleeping bag has to keep you warm at night.
For most people, finding the right gear is an iterative process -- you buy inexpensive gear to start, of course, then replace things gradually as you realize what you need and want. This is true with any sport or hobby, I think. It's more difficult when you're young and on a limited budget, and saving all your money for a long hike. It's even more difficult when you can't easily test the gear under realistic conditions, e.g. testing a sleeping bag in cold weather, or trail shoes on a steep climb.
So, first, a question: where are you planning on doing your increasingly longer hikes to prepare?
Second, a suggestion: plan to go for a week long, or even two week, hike on the AT in Georgia next spring or early summer. Save up all your money for gear, and bring it to the
outfitter at Neels Gap, which is one of the best places to buy the specialized gear that long distance hikers use. Let them sell you all the gear you need for a thru-hike - they will make sure it fits, make sure you know how to use it, and you'll get the right gear for the hike (or, at least, you won't get totally wrong gear like you might at a big box store). The folks here on WB can help you put together a list, and figure out what you already own that will work, and where to save money.
(This reminds me, several years ago we met an older gentleman on the trail in GA who had done exactly that, and he was from New Orleans.)
Beyond just getting the gear, the week long hike will give you a very good idea of what to expect on the trail, and how your dog handles the hiking life day in and day out. It's very different.
Good luck.