Several comments, but I'll try to be brief:
1. I see no issue with you doing it yourself, even if it takes a while. Big city people (of which I are one

tend to be a lot less patient than small town folks.
2. I agree with salvaging what you can, BUT - and this 'but' is as big as the one on Kim Kardashian - know when to stop. Urine soaked floors? Pass! Old studs most likely are not standard dimensions and will either have to be resawn (which will cost you more in damaged saw blades than the wood is worth) or used as is - if that's even possible. Pass! In other words, pull the easy and valuable stuff out, but forget about salvaging much usable building material. It just isn't there.
3. If you're gonna do it yourself, buy BOTH a dump trailer and a tractor/backhoe or bobcat. You don't want to handle all of that material by hand even if you ARE young and strong (you didn't say?). If you don't need 'em when you're done for snow removal or other work you can sell 'em - maybe even for more than you paid for them since you'll likely have fixed them up some, what with being a GJ member and all.
Once you get the valuables out you can carefully weaken the structure (if that's even necessary) and then use a chain to pull the structure over and away from your house, or carefully push it with the loader. Once it's on the ground you can pick up bucket-fulls at a time and sort through things if you want.
Plus, it's a GREAT sense of accomplishment to see the structure on the ground. It always looks a lot smaller and more manageable to me, and seems easier to clean up.
Good luck in whatever you decide to do, but remember:
