Luxy,
is that budget including everything needed to get it to work?
Think not just wheels, tyres and lift, but allow for SYE (& driveshaft), flares, ratios and lockers....do the sums and I think you'll find that list a bit more......Just trying to keep things realistic......
As for the lift - my PERSONAL 2cents I would not go over 5" lift. Now that's just a personal pref but I can name many place a "smaller" lift will out perform the larger lift....remember bigger ain't always better