I think you need to separate this into two parts: Money spent before the trail starts, and budgeting while on the trail.
Before you start, you're going to spend money on gear for sure. Your sleeping bag that was good enough for a weekend trip is now your home... Do you really want to put up with that limp, cold bag for 5-6 months? Same goes with a lot of things. Every book you read about the AT is going to suggest you cut the weight as much as possible, in order to increase you chances of success. If you can buy new lightweight gear, particularly tent/backpack/sleeping bag, and that saves you 5-6lbs on your back, it's huge. Of course, that's also the most expensive stuff :) That being said, there are cheaper and more expensive options for everything! As an example, Walmart brand blue foam mats are $5-10, very light, and do the job for many people. Thermarest (and others) make inflatable, very light, high R value mats that are infinitely more comfortable, but cost $100-150. Literally every piece of gear is like this :)
So, for gear buying:
- Bare-bones: Assuming you can leverage much existing gear, < $500
- Average: Needing to replace most things, but not always choosing the best stuff: $2,000-3,000
- Luxury: Buy the best of everything, $3,000-4,000
For actually hiking the trail:
- Bare-bones: No hostels, town-days kept to a minimum, pre-buy all food in bulk and have it shipped to you. Minimize new shoes/socks (maybe 4-5 pairs of shoes total?). Hike faster to make the trip shorter, so aim for 5 months at $500/month. $2500.
- Average: 10-15 zeros with a hostel and occasional shared motel. Buy most food as you go, ship some food from home to expensive areas. 6 months @ $1000/month. $6000.
- Luxury: 10-15 zeroes with regular motel rooms to yourself. Stop in every town for a bite to eat. Replace all your gear as you go with lighter gear. Buy a round of beers for your friends :) Carry 2 of everything, take 9 months, 3 kinds of maps, 2 cook pots, and a sherpa or two. Cost: sky's the limit!
One other fixed cost, transportation to/from the trail: For me, that means 2 one-way flights at ~$400/each.