For the demo party, I'd prioritize things that you can't do without help- anything unwieldy like carpet, or anything heavy like appliances.
If you have a reciprocating saw, cabinets can be taken out a little at a time by one person.
Re the linoleum floors- it would depend on the height difference. If the entryway and bathrooms have a thicker sub-floor to make up for the carpet, you'd want to get as much of the existing floor up as possible- nothing worse than stubbing your toe on the floor as you enter a room, or that sick instant when you put your foot down and the floor's not where you expect it to be.
As to what to DIY, that depends on your skill / comfort level. There are a few things that I personally refuse to do- roofing and tile to name two (too damn old, too out of shape.) If your crew is 1.5 folks, you might think about getting help with those windows and doors. They can be heavier than you'd expect. Same with the tub
As to sources, etc- is this going to be your primary residence, like right now, or are you living elsewhere while you get this ready to move in? You can get some really good deals through habitat for humanity's re-store, but it's not a big box store that has one of everything- you might have to find a couple nearby locations and keep hitting them once a week until you can find what you need. You can also keep an eye on craigslist- if you're comfortable evaluating used / semi-used materials, it can be a great way to get things on the cheap.
If I were in the area, I'd be happy to help. Sadly, I'm in Texas.