You seem set on a DMR. They require quite a bit of investment (Minimum a new barrel, compression system, optics) to outperform your standard AEG. Most "DMR" guns, like the M14, G3, or SR-25 start at $500, and with $200 worth of upgrades required to get it performing like an airsoft DMR, it puts them well out of your price range.
That said, I'd recommend starting out with a basic, all-around performing assault rifle and game it for a while so you can see if you actually like airsoft. The Umarex G36 your friend wants is a solid gun, and most people on here recommend the King Arms M4
as an excellent and inexpensive choice for someone starting out.
Seeing how you're going to be "rolling together" with your friend it might help to use guns that use the same magazines and batteries. The Umarex G36 can be fitted with a $20 part that allows it to use standard M4 magazines, and takes the same mini battery as a M4 does.
Hope that helps a bit