Are you sure you really need 37s? The difference between 35s and 37s is a whole can of worms. Is this going to be used for wheeling or mostly looks? If you plan to wheel on 37s then you need to address the weaknesses in the front axle. You'll need better better ball joints (Teraflex, Rare Parts or Dynatrac) because the stock ones won't last 10K miles with 37's that have proper backspacing. The inner Cs will also need gussets and the axles tubes trussed or at the least sleeved. Best bet is the Artec Industries truss kit.
If you use exhaust spacers or a new crossover pipe you can go up to 3" of actual lift before the front driveshaft starts to have issues. An option to increase this some is to replace the factor Rzeppa joint with the Teraflex high angle one. You could then run a 3.5" lift with the stock (other than the Rzeppa joint) driveshaft.
You can clear 37s with a 3.5" lift. That's not necessarily long arm territory. A good short arm kit with adjustable arms will be fine especially if you use geometry correcting drop brackets. You'll also want to get the track bar heights corrected so the roll center will at OEM specs or better. Once your geometry is correct most of the ride quality is in the tuning between the springs and shocks. Of the lift manufacturers you listed, all of them tune their shocks to the springs. You really can't go wrong with RK, Teraflex, or Metal Cloak.
Turning 37s is no joke. You might want to consider hydro assist steering or at least bracing the sector shaft on the steering box. JKS Manufacturing makes a very nice and complete sector shaft bracing kit.
Next you'll want to regear the axles because with 37s even 4.10 gears are not enough for most people. I know guys that say they can get by with 4.10 gears with the WA580 auto on 35s, but not 37s. Whether you get the auto or manual, you should be looking at 4.88 gears to run 37s. If you do all the above correctly to avoid the mistakes of the past, then you'll need to at least double your budget. You still sure you want 37s?