First of all, when are you going? The price you pay depends upon the time of year that you go and also how close you are to Disney. You need to get an idea of number of bedrooms,amenities (free phone calls, big screen tv, wireless internet etc.) ; whether you want a resort with maid service or whether you want self-catering meaning you look after yourself the same as you would at home.
As for some of your questions: everything is supplied: pots, pans, bedding, towels etc. You don't need to bring anything except for things like toilet paper, paper towels, soap etc. There's always some to start with but you have to buy more yourself. Where you pick up the key depends on the owners/company, sometimes there's a small coded box with the key in, sometimes you pick it up at the management company, or front desk if there is such a thing. With a self-catering condo sometimes you're asked to strip the beds and start a load of laundry before you leave, sometimes not.
There's places like the Mariott properties that you rent through them like a hotel, or some Management companies rent out privately owned properties that they manage for the owners or you can rent directly from the owners themselves. We usually rent directly from the owners from sites such as vrbo.com, homeaway.com, fabvillas.com, windsorhillsrent.com ,
www.windsor-palms-florida-net ,
www.StayAtEmeraldIsland.com and many more.
Subdivisions with condos will have a community pool area and resort-like amenities: Emerald Island, Windsor Hills, Windsor Palms, Terra Verde, Encantada etc.
This is the listing page for the vrbo.com site for the Kissimmee area:
http://www.vrbo.com/vacation-rentals/usa/florida/central-disney-orlando/kissimmee
You have to narrow down what kind of place you want, what amenities you want, where you want it, how much you want to pay.
Here's a map that shows you where the subdivisions are:
http://www.1stfororlando.com/Location-map.htm
After you figure some of that stuff out put another post on these boards and someone can help you with the renting process. Good Luck!
