For a 20" wheel, stock tire size on the 1500's is 275/55r20. 275 is your tire width, essentially, in millimeters. At 25.4 millimeters per inch, that's 10.82 inches wide. The 55 is the sidewall height, in a %age of the width. In this case, 275/55 means 151.25mm, or 5.95 inches. That's the distance from the outer edge of the rim, to the outer edge (driving surface) of the tire. Since there's tire above and below (all around, really) the rim, we double that number, and then add the rim height (20 inches, in this case) to get overall tire height (5.95+5.95+20=31.9" overall tire diameter). This is just a general math, though...different brands end up coming out sized slightly differently with the same size measurements, due to tread depth differences and what not. So the stock tire size for the 20" wheel is essentially 31.9"x10.82" r20 (275/55r20).
275/55/r20 fits fine, zero rub, stock. You COULD get the 20" wheels you want, and put 275/55r20s on to be safe and get one step of the whole upgrade done immediately, and then continue to save money until you have the cash for the tires you actually want, plus the lift. With the RCX 3.5" lift, you're looking at like $500+ for the kit after shipping, probably 400-500 bucks to install if you can't do it yourself, around 75-100 for an alignment, 1200+ for the XD Monster 20" wheels, and even cheaper decent, non-AT tires are going to cost you at least $900 for a set of 4, mounted and balanced, more if you need to transfer your TPMS sensors, and quite a bit more yet if you need to buy 4 new sensors. So you're looking total at around...3 grand on the low end, 3500 more realistically. If you're balking at $1200 for tires, when at the very least you're going to have to spend $800-900 anyhow for a decent set, I'm sorry to burst your bubble but the extra ~400 for high quality A/Ts is just a drop in the proverbial puddle. Your truck can look awesome with just the lift, the wheels, and some decent tires...but if you really want looks that set it apart, and actual offroad capability, the A/Ts are kind of a must, imo.
Personally, I'm getting rid of the 20's that came with my truck as soon as I get money saved, because A) I actually like 17's on a 4x4 better, and B) I can buy 4 tires and wheels in a combo for around the same price I'd pay just for tires @ 20 inch, and have more options (hard to find tire sizes that will work for me in a 20" wheel, whereas the 17" wheel has a bazillion tire size options).
In the end, it's a matter of taste and doing what makes you happy. I hope you find what you're looking for, though I recommend you raise your expectations to at least $225-250\tire if you want -decent- All Terrains, and that'd be a pretty good bargain. Most of the ones I like are between 289 and 365\tire in the 20" wheel sizes. Check around your area too, a lot of tire shops do buy 3 get one free tire sales, for a $300 tire that effectively brings your costs down to $900 for 4 tires, or 225\tire. If you're patient, and shop smart instead of impulsively, you can save big bucks. Also look to save by doing a wheel and tire package, or find a place that does mounting and balancing free (a lot of places will charge 20-30 bucks\tire on aluminum wheels, while some may do it free if you buy the package from them. Another 80-120 saved if you can get it.) A lot of online shops do mounting and balancing free with tire\wheel packages...I believe Tirerack does, or at least they used to.
If you're just looking for a decent tire in 20" that will get you by until you can afford the lift and high quality A/Ts, try Mastercraft Courser AXT 275/55r20. My buddy uses these, and likes them well enough. Gets a lot of life out of them, too, and they can be had for around 180-200\tire. I presently have Mastercraft Courser MSR 275/55r20s mounted on my Sierra, stock other than an exhaust. My dad had bought them before I bought the truck from him, last november in anticipation of bad snow (one on it when he bought the truck were apparently a crappy summer highway tire, did awful in bad weather.) They're fairly aggressive looking, and get good enough offroad\mud traction to pull my 94 C3500 diesel and hitched 12" chipper outta 18" of mud without any problems. Still, on a 20" wheel there's not a lot of "meat" to the tire in that size, but you really can't fit much bigger under there without rubbing without at least a leveling kit.
Sorry for rambling a bit. Been up touch over 24 hours now, and for some reason still can't sleep.
Edit: If you buy a leveling kit, you'll have to remove it to install the lift kit, they won't work together. So if you intend to lift in the near future, a level may be a waste of money. If you install the RCX 2" level yourself, the part is only $60-some bucks, but you'll still need to do an alignment...depending on shops in your area, that could be $60, or $100. If you can't do it yourself, you're looking at 80-160 bucks (again, depending on shops in your area) to do the install. So between $140-320, for a leveling kit you intend to get rid of soon anyhow, may not be a wise investment, especially since you're looking to pinch pennies already wherever you can on this overall modification.