You gays are getting ahead of mothercoder.
Mothercoder, have you selected a trailer size? That will determine costs to do things. I would follow Bob's lead on sizing if your toad can pull it. You can talk to trailer sellers and see if they offer empty trailers with no interior siding. You may even be able to request insulated interior. I read in another thread that you are, or were, in the DC area. Being that far north, the winters get bad so it may be a viable option for you.
First, define your electrical by looking around your current home. Then really consider what you need. If your needs are low, you can get an inverter and plug directly into it and not have any 110/120 volt house wiring. I didn't use house voltage 110/120 when I had my truck campers. I did all my cooking on a small Coleman stove, either propane or white gas (Coleman fuel in the red can). My lighting was 12v incandescent or LED. I had a 12-volt car radio set up in a box with two 4 inch speakers and a small under dash car antenna. Now, you can buy cheap radios for $10 that have the option of charging from 12v. TV's can be bought that is 12V and some can be run by 12v or house power. I'm not a TV guy so no need for that for me. Phones, tablets, and laptops can be charged from 12v. Most anything that you can think of can usually be run on 12 volts or a small inverter. You may need a true sinewave for certain electronics. So really think about what you need. Solar is something to consider after getting your electrical in and make sure what you have is what you need. Then the solar system can be sized for the intended systems.
Plumbing is no big deal unless you're after a full inside shower and house style toilet. I've done the bucket toilet, homemade camp potty, and the Thetford porta-potty. All very cheap considering what they are. I do like a running sink water for hand washing, teeth brushing, and food prep. I like the foot pump type faucet and a cheap medium size stainless steel bowl cut into the countertop and a drain fitted to the bottom. Five gallons of clean water on one side and a five-gallon waste water jug under the counter to catch the contents from the sink. Some people simply run the drain straight out of the bottom of their home. A lot of places frown on the direct discharge of gray water.
You need to define your intended usage of the trailer for insulation. If your plans are to follow the weather, 50 to 80 degrees, you can get away with 1/2 inch foam and some thin covering on the walls and ceiling. One thing that helps tremendously, is coating the roof with a elastomeric coating to help block out heat. It works like a dream. I frown on fiberglass insulation. It has a tendency to compress inside a moving vehicle and it also breaks apart. That puts fiberglass fibers in your living area and breathing it can be dangerous. The best insulating job I had turn out on floors was 1/2 inch foil faced foam, foil side up. Then covered with 7/16 OSB smooth side up, and covered with a rolled vinyl flooring. I taped all seams of the insulation and OSB with foil tape. I also staggered the breaks between the OSB so they wouldn't line up with the breaks between the foam insulation. Cheap vinyl squares or strips don't last long in a mobile vehicle. The heat causes the glue to let go. Then they slide around or stick to your feet when you walk on them.
Another consideration is buying a tongue box for the trailer. You can store and vent your batteries inside, along with a jack, spare tire, lug wrench, and propane if you use it. The spare can be monted under the tongue but needs to be securely mounted. They have a habit of walking off around here. It's always good to keep a few spare parts in there too, replacement lights, bulbs, lens for lights, and extra electrical connector for the vehicle to trailer wiring. It only takes hitting a piece of tire on the road to damage lower mounted lights and sometimes the electrical plug between the vehicle and trailer.
I'm sure this doesn't cover it all, but it should give you some more things to think about.
