My family and I lived in our RV for 2 years travelling around the U.S.. We stopped last August. We also have spent many long summer trips as well, if you have any specific questions let me know. I had a really long thread about it a while back you may be interested in reading.
* are trailer park people weird?
It really depends on the trailer park. Most of the time no, no weirder than regular people, especially if you're staying at a resort/vacation type RV park. When you stay at parks that have a higher percentage of full time permanent residents then the Twilight Zoner factor increases. It you are sticking to mainly KOA's, state parks, family resort type parks then most people will be either retirees or families like yourself. If you're staying at the cheapest place you can and 80% of the people are living there then you're trying to vacation amidst a group of people having a hard time just getting by, it can be weird.
* after you factor in decreased gas mileage, campground fees, maintenance, storage costs, etc., is it really any cheaper than just getting a hotel room?
I think it depends how often you use it. If you go out a few weekends a year, then no. If you go a few weeks a years for vacation, some long summer weekends, and as often as you can then it can be worth it. We lived in ours and we store it in our yard so no fees. However, cost isn't the only benefit. The RV vacation is much different than hotels. You're sleeping in your own bed, in your own kitchen, cooking food, closer to nature, campfires, getting to know people around you. If you're talking economics it probably isn't worth it for most people who don't use their rig enough, but economics isn't the reason most people RV, it's the type of vacation they're looking for.
*how does the shower situation work? Does it have a big tank that you can fill up with a garden hose? Does the water get hot?
RV showers, unless you have a REALLY expensive rig, are horrible. We lived in ours for 2 years and our shower was a storage closet. We always used the campground bath house. Not only is the shower small and no water pressure but the tank ran out super quick. We tried it once when we first got it and never used it again. Everything else (kitchen, toilet, tv, beds) were fine but shower was a joke.
Campground showers are a whole other discussion, everything from giant, clean personal bathrooms to places I'd rather give myself a sink bath in a Venice beach public restroom than shower in.
* Renting
If you can afford to rent I would do it, RVing isn't for everyone and it's a big investment if you're not sure. Before my wife and I bought ours we actually rented onsite. The places where you rent and RV and drive where you want are really expensive. However, a lot of camprounds will have rental units on site. YOu don't get the experience of driving it, but you do get to live in it for a few nights and see what RV living is like. Cooking in the small kitchen, the rocking of the "boat" every time someone gets up to pee, living close to your neighbords, the little shower, etc.. It's the most economical way to try it out.
* SIze
Picking the type and size of RV are completely subjective based on what you want. If you want to travel into really remote, backwoods places or visit cities and be able to move around easily then go as small as you can live in. If you want to spend long trips with your family and invite people to the RV and have huge tailgate parties then go as big as you can afford. We lived in a 32' Fifth Wheel with 3 kids, it was a bunkhouse. It was a nice size but when you go that big you can't just pull off the side of the road and check out things spontaneously, you need to know where you're going, what the road is like, if you can turn around, etc.. If it was just my wife and I, i would go smaller for more maneuverability and freedom to be more spontaneous. For what we did our size was probably just right.