I would reccomend renting from an outside vendor. That way you know you have the
ECV. If you rent in the parks, there is always a chance they will be out when you get there. If you park hop, or if you leave at mid-day to go back to the hotel, you have to turn it in and hope there will be one later.
Taking it in a car is totally feasible. If you are going to do this, make sure you discuss it with whoever you rent your ECV from. Some are designed to easily take apart and load into the trunk. One piece will be a little large, and a couple will be heavy, but the heaviest will probably be around 30-35 pounds. It should fit in most cars -- my Pride Go-Go Elite Traveller fits very easily in the trunk of my Hyundai. If you don't need it at the hotel, you can leave most of it in the car and just take in the battery to charge every evening.
Riding on the monorail with the ECV is very easy. You do need some help -- a CM sets up a ramp over the gap, and you drive straight in. They ask where you want to get off and radio ahead, so that at your destination, a CM sets up the ramp and you back straight off.
Riding the bus is a little trickier, as you need to essentially parallel park on the bus. The bus "kneels down", a ramp is extended, you drive straight on and park. The driver then straps down the ECV. You should move to another seat -- when riding the ECV the center of gravity is too high and it might try to tip. Most people catch on pretty quick, just make sure you turn the speed way down. If there is someone in your party you think might be better at it, they can drive it on and park it for you.
One other caveat about busses: they are limited in the number of
ECVs they can only take 2 or 3 at one time. If you are on a route with multiple stops, your chances of being able to load are better if you are at the first stop. For example, better to be at POFQ rather than POR, because the busses hit that stop first.
If you chose not to rent a car, you are not limited to Disney transportation. If you have an early ADR you are worried about making, for example, Mears has taxis designed to transport ECVs that you don't even have to take it apart for.
You can always park your ECV to go on a ride or into a crowded store on foot. You can park in stroller parking or any out of the way spot. Just take your key and any valuables with you. Do be aware that sometimes a CM will move it, for maximum use of space, so if it's not where you left it, just look around. Also consider the length of the ride line, though -- Soarin' has a line 1/4 mile in and 1/4 mile back out. It's the worst, but some can be pretty long.