yes, a place to sleep, diapers, and a car seat and you're good to go!
target does have cloth diapers but i wouldn't really recommend them being used as diapers...well the DSQ gerber prefolds aren't awful (i've seen those there once or twice), but if you're gonna go the prefold route, get some that are really absorbant, and some good covers, and you'll be much happier and probably more likely to stick with it.
we only have a couple crib sheets but he rarely actually sleeps in the co-sleeper so i don't have to change them that often. the Diaper Champ is great for holiding dirty cloth diapers as well as disposables (i put a nylon laundry bag in it for the cloth diapers and a trash bag for disposables). haven't needed to use a thermometer yet, but we've used lots of tylenol and motrin drops (teething) and mylican anti-gas drops. never used a wipe warmer - no place to plug one in near the changing station and no room for it anyway.
consignment shops have lots of the "gadgets" - exersaucers, johnny-jumpups, etc. both of those have been worth purchasing IMHO - allows me to put him down so i can fix dinner, check email, take a shower, etc. especially the jumper. my god he loves the jumper.
but the best $40 i spent was on my sling. actually in retrospect, i wish i'd gotten the kangaroo korner adjustable fleece pouch instead of the new native baby carrier but the new native made more sense for summer. he never did like the baby bjorn, and the sling saved me on more occasions than i can count. he'd get fussy right around dinner, and i could put him in there, swing him around to my back, and keep cooking. and we'd go on walks and he'd fall asleep instantly. i still use it pretty much daily (not my new native though, but a fleece one my mom made me out of a blanket from costco)
as for where to register, i registered at babies-r-us (bleah, but accessible through amazon.com too, so i listed bunches of kids books i wanted too) and made my own list of links through wishlist.com (diapers at babiesinthesun.com, assorted stuff at organicbebe.com, etc.)