There's nothing wrong with getting an XT, but for the sake of economy, also consider the DeoreLX. If it's adjusted well, it'll still work well.
To adjust the rear derailleur, first get the add-on derailleur hanger you'll need, and attach it like your old derailleur's built-in one did (if this is your first time working with these, take careful note of how the old one was).
Now you should have the derailleur hanger bolted into the axle slot, and the rear wheel on the bike. Before going further, note the little "tail" with the adjuster screw, hanging right off the derailleur's upper pivot bolt. Watch this screw carefully as you begin to thread the derailleur into the hanger, the derailleur must be swung back far enough that this screw misses the derailleur hanger entirely, or you'll be a hurtin' unit!
Once the derailleur is safely onto the plate, use a 3mm allen key to remove the lower pulley from the derailleur, so you can route your chain through it. While you've got the cage open, note that the inner cage plate has a metal "finger" that keeps the chain in, not only behind the bottom pulley, but also right below the top pulley. Make sure the chain runs on the proper side of this finger.
Now you should have the chain properly routed. Before hooking up the shift cable at all, grab your #2 Phillips screwdriver and use the H limit screw to limit the stroke so the chain happily rides on the small cog without clatter, but doesn't want to fall off to the outside. Usually, if you sight from the rear of the bike, it will appear that the derailleur's upper pulley is just a bit further out than the teeth of the small cog, perhaps 1mm or so. This step ensures that even if your cable slipped, the derailleur still will not go past the small cog.
Now pedal and shove the derailleur inboard by hand to the big cog, and stop. Use the L limit screw to limit this end of the stroke.
Now shift your shifter to the high gear (8, in your case) so that the cable is as relaxed as possible. Run the adjuster barrels into the derailleur and the shifter as far as they go, then back them out maybe 2 turns so you have a little leeway later. Run the cable through the derailleur's adjuster barrel and fasten it down on the correct side of the cable-anchor bolt (for an XT or an LX, that would be the inboard side). Snug down the cable-anchor bolt moderately tight while pulling firmly on the cable to draw it taut.
Next, click the shifter one click, from 8 to 7. What you want is for this to produce exactly one shift. Chances are, it will clatter-clatter-clatter and maybe shift. If necessary, dial the adjuster barrel on the rear derailleur counter-clockwise a turn or two, until the derailleur runs quietly in the second cog while the shifter is on 7.
Keep shifting inboard to the second-to-last cog, dial the derailleur's adjuster barrel counterclockwise until you hear a faint noise of the chain rubbing on the side of the big cog, and then turn the adjuster barrel back clockwise about 1/2 turn or until the noise stops. Test the shifting in this position, both upshifting and downshifting. If the upshifts are hesitant, crank the adjuster barrel clockwise 1/2 turn and try again, until it's right.
Finally, put the bike in the lowest gear: inboard chainring, inboard rear cog. Pedal backwards. Does the system go bump-bump-bump as the teeth of the large cog reach through the chain and touch the teeth of the upper pulley? If so, screw in the B-tension screw most of the way and test again. If it still won't behave, you may need to shorten the chain, but don't shorten it so much that it cannot wrap around the largest-size cog and chainring at the same time.
All of those steps are founded on the premise that the derailleur hanger is in alignment when the wheel is bolted down. If you get the derailleur onto the mount and it looks like it's not parallel to the rest of the frame, then you may want to take the derailleur off again and use an adjustable wrench to carefully realign the mount.
You said your system was skipping, and a second cause of that would be a worn chain on a brand-new cassette. Did you put a new chain on when you got the new cassette? If not, might want to pick one up.