Welcome.
If you are not planning on replacing your SUV, you must first learn the towing capacities and equipment that you have. I would start in the owner's manual. Learn what you can about weight ratings and understand the limitations of your SUV. You then need to know what equipment is already installed on your SUV, like the hitch, it's size, it's capacity and whether or not you have trailer light wiring.
Armed with that knowledge you can then start searching for a towable camper. Internet searching and learning is a good start to be a little educated before you interact with sales people. Finding a sales person you can trust is like looking for a unicorn, so being armed with more knowledge that they have is recommended. Some sites to learn from are the internet sales sites, like RVTrader.com. Then you can hone in on the manufacturer and specifics that meet YOUR needs. Once narrowed down, going to the sales lots can much more rewarding and a little less overwhelming.
Your concerns about power and connections. Electric power available at the campground is the simplest solution. If you are planning on boondocking and not having electric water or sewer connections is a whole other topic you'll need to research. Solar, generators and holding tanks. So much to learn and decide. Making the connections is rather straight forward, with some upfront guidance.
Good luck, and as you progress, keep us in the loop. We're here to help. At one time, we were all beginners.
Please update your profile to include your SUV and soon-to-be camper, so we can have a better idea what we're working with.