Haha, thats funny, because Im planning on doing the same thing, if you live in california we should get together and talk. So the biggest van you can buy is an Econoline Clubwagon or e350 extended, you would also want an extended top which gives more head clearance. If you get one of these vans which I just bought one recently, you can easily put a mattress in there, although I would suggest building a sleeping area instead as to not take up so much room just for a bed. If you build a custom bed area in the back, you can put some cabinets in, a sink, refrig , but unforutnately I dont think there are any showers available in ANY of the vans. If money isnt an issue with you, I would suggest getting a 4x4 van, as those are usually built for excursion purposes and come with sinks, generators, sleeping area, caibnets, and evrything else, except for shower . As for the shower part, I plan on using local gyms for that purpose, get a membership, use it for taking showers and cleaning up, working out or whatever, and they are pretty much anywhere you would plan on going, a shower COULD be built in a van, but it wouldnt be easy, and you would need a very high top. Maybe a motorhome would suit your needs better. I looked around for months before I found the van size I needed, there is no bigger van than the one I have mentioned, again, if money isnt a problem, get a 4x4 extended Ford E350 or Clubwagon, they can range from 15,000 to 50,000, maybe you can get one for under 10,000, but it would probably need some work, I bought a 90 Ford clubwagon E350 extended with extended top for 1000 bucks, but I have since put 1000 to try and get it running the way it should be, by the end I plan on having a sink, bed, cabinets, refrigerator, etc, but I will probably end up having spent 1000 more, but I am also doing all the work myself which saves a lot of money.
For electrical power, you would want to get an inverter, which will probably cost about 200 bucks but will be sufficient to power lots of things in there, also I would suggest installing an extra battery, and a solar panel mounted on the top of the van, this will keep your electrical neeeds satisfied. This can be very extensive to fabricate or have someone install, its not that hard to do it yourself, a little research and some planning will take you a long way, air conditioning most cars already have, so I dont think you would have to worry about that one, unless you wanted to install one of those top mounted ones.
As for cooking, if you like bbq's that would be your best bet, get an axe, chop some wood from your local forest, get a magnifying glass and start a fire, now get a pan and a camp grill and your ready to eat. Otherwise you would probably need to install some typpe of propane tank grill, or get one of those single electrical stove tops for about 30 bucks and plug it into the inverter. You dont want to install to many electrical gadgets in your van unless someone professional is doing it, it could be a fire hazard and you dont want your home burning down.