First, talk to other folks that had vinyl siding installed and see how they're pleased w/their job. It's one thing if the material isn't top-rate and another thing if the job was still a good one. Make sure you can 'sift' through their answer.
The thinner the siding is, the more it will expand and shrink. I live in the NE so I bought vinyl that was .044mil in thickness. That was the minimum, and I really didn't need it to be thicker.
Consider having Sill Cocks (outside spiggots) and Electrical Blocks added at the time of the job to all 4 sides of the house (or at least the front and rear. Later on, you can add the hardware if you aren't having this done when the vinly is installed. For me, I have water now on 3 of 4 sides and electrical on all 4 sides. It has cut down the use of extension cords and hose extensions quite a bit!
Buy a little extra siding. You never know when you 'll have to repair/replace damaged siding. It's not unusual for a particular 'style' to go out of popularity no matter how hard a Salesman tells you it won't. The same goes for extra J-channel, soffit, 'blocks' (that I mentioned above), and so on. Once you get a Materials List from your Contractor, you can ask him to buy a few extra pieces. Make sure you specify FULL pieces and NOT scraps!
As far as installation procedures, it's BEST to have your siding installed on a flat, smooth surface. IN fact, most MFGRS. require it or the Warranty can be VOID. Soooo, BEFORE you pay for anything, 1) read the Warrany and Installation Instructions, and 2) review them w/your Contractor. You should feel comfortable 'specifying/hashing' the Warranty and Installation Instructions w/the Contractor BEFORE he begins the work. At my home, I removed 22 squares (1 square = 10' x 10') of Asbestos Cement Shingling and added 1/2" of rigid foam insulation in 4' x 8' panels. I taped the seams and then installed the siding.
Talk about what the Contractor is going to do about the waste. Make sure it's NOT a sudden last-minute charge to your bill. Consider having new gutters installed. I'd go with SEAMLESS gutters and hidden hangers. Oh, be sure you trim back all the vegetation ALL around the house before the work begins. Otherwise, your Contractor may bill you for that or try to 'work around' those things and end up w/a crappy job. Decks are especially tough to work around. I removed 3 planks on my deck and did the job right. If you have the same, talk to your Pro about that too.
As far as a good MFGR., Ashland-Davis (Certainteed) and Woolverine are pretty good. Visit the Vinyl Siding Institute for more info. It is, of course, a bit biased but still a good source for info. If you have more ?'s, post back.