That's an excellent question. Hmmmm...let's see:

Pack $150
Tent 200
Sleeping pad 75
Sleeping bag 150
Canister stove and pots 100
Water filter and bottles 75

Total $750

This will trigger a huge number of replies, split equally between those who say I'm $500 too high and $500 too low. I didn't go look up any exact prices, but for high-quality, not-too-heavy gear, like the brands in my previous post, this should be about right in total. The pack may be a little less, and the sleeping bag a little more, etc. My estimating errors will probably leave enough in the budget for all the little stuff like compasses, first aid kits, pocketknife, and such.

You can save some money by shopping the gear-for-sale part of these forums. People here are pretty honest about the condition of the gear they're selling, and will usually tell you why they're getting rid of it. (Often, it's because there's something new and shiny they want.)

A lot of the clothing you already have, like longjohns, windbreakers, gloves, and hats, will be very functional for backpacking. You may or may not need a pair of boots or trail shoes; $100 - $150 will get you into something pretty good.