You get what you pay for and putting a "budget" on your upgrades only wastes your time and money in the long run.
My advice, find a dealer that sells upgraded vehicles. Go for a test drive and make a decision on how the ride will suit you. I took out a dealer Jeep with a 3" Mopar lift and it's great for a DD and off road. Not in your budget.
Rubicon express was the previous Mopar supplier and now Teraflex. OME (Old Man Emu) and AEV are good as well. I've seen just the shocks cost way more than $479, so don't expect much from a "complete kit" that is under $600.
JK "Unlimited" is a bit mi$$leading...
- any kit that cheap with shocks worry's me
- drop pitman arm and assuming a drop TB bracket. This is to correct geometry, which is not always needed. DPA's cause more issues anyways. Avoid at all cost.
There's a ton of information on this forum, I'd suggest poking around a bit and getting some knowledge. That said, I've been doing a lot of research myself for my wife's JK (on order), and will probably go with the AEV 2.5 lift. It's just under $1k, but I'll add geometry correction brackets, either rancho or AEV, for another $100ish. This kit gets very good reviews everywhere I've seen.
You do not need a lift to run 33's, let alone a 3". If you want a lift then I suggest a 1.5" or leveling kit. Even a 1.75" budget boost. You can keep your stock shocks or invest in some nice ones. You will have a great riding Jeep and plenty capable.