First of all, Welcome! to VDF. Congrats for the new life and being responsible about bringing one in to the world. Now, down to the biz of biz. The cymbals are worth, ready for this....? MORE than the drums. I would sell them separately. The drums are worth about $150, tops. Sorry dude, just the market today. The cymbals, the rest of the boys and girls would have to give you the skinny on them, but $300ish or more (if they are all Zildjians) would not be an unreasonable expectation I should think, if the hi-hats are decent. Don't let anyone sneak up on you and steal them from you....it does happen on here from time to time. Me, I'd think real hard about selling the cymbals as a complete deal, that way you don't end up with 1 left and nothing to do with it but hang it on the wall...or not, just whatever works for you.
Looks like you've got 13" hats, a 13 and 14 crash and an 16 or 18" crash/ride? The big one is a nice looking cymbal. IF you try to clean it, DO NOT use steel wool, a 3-M scratch pad or anything abrasive, just rinse them off with soapy water and a soft cloth.
And if you decide to clean any other parts, just wipe them down, leave the tear-down to someone else that knows the routine...do you have the parts for the bottom heads? If you encounter ANY problems selling the drums, send me a private message, you might end up just donating them to a music school or broke kid....just how we do it sometimes my man (I "give away" 3-5 complete drum sets a year, and I'm seriously broke, but other forum members also donate parts and pieces to me so that my little mission can continue)...pay it forward for some kid that can't, if you can afford to do so, if not, it's OK because we all know how it is out here.