As far as time goes, figure about a month. I thru-hiked this past summer with a friend in 3 weeks exactly, but we put in some long (18+) days and if i do it again (which i might soon) I will take a full month. There are tons of cool spots where I would’ve loved to hang out but had to move on to make a deadline.
The cost of a trip like this has much to do with how prepared you are. including last-minute gear buys (summer bag, bag liner, poles), food, herbal provisions, and a few in-town meals I probably spent around $600, give or take.
This summer I’ll either do the LT again or the Northern 500 miles of the AT and I plan on keeping is under $500 either way, because i don’t need any new gear. I’ll probably use the same shoes, even.
It depends on how much gear you still need and what lifestyle you’ll be living on the trail, but you can get away with less than $100 a week on trail no problem if you’re in the woods 5 or 6 days out of 7, all vices included.
physically, there’s no way to know until you’re out there, but what kind of mileage are you doing on your 2 night trips? maybe try a longer trip and see how you like being in the woods for a full week before planning your pace.
At the end of the day, though, it’s just walking.
Doyle