You would never make it so buy an RV !
I'd disregard whatever captain mike had to say - kind of a knuckleheaded comment with no real content except a 'bah-humbug' - you can totally get all of the things you are asking about in a liveaboard situation.
Lots of boats have showers. I have a five gallon hot water tank, and make hot water both when I motor, and when I am plugged into shorepower. I have pressurized hot and cold water onboard, and a built-in shower insert, with an electric shower pump-out. Works fine - just wipe it down when you're done showering to avoid mildew problems, and your head (bathroom) is squeeky clean, every day.
Lots of boaters cook with propane - it's quick, powerful, easy-to-use, and a 20 lb tank lasts a very long time. Just open a hatch while you cook to vent the carbon monoxide and cooking odors out of your cabin. I try not to fry or cook greasy things down below, and save those for the outdoor BBQ, because I don't want the odors permeating the fabrics in by cabin.
As for internet / cable, tons of marinas have this. When you are out cruising, broadband xpress services almost every Marina on the west coast (not sure about the east coast) and that gives you three miles line-of-sight service from the marina office, or more depending on how high you mount your antenna - this is a subscription service, but they have short-term packages available. That, and tons of private ocean-front homes have unsecured wireless networks that you can jump onto to check your email, etc.
So in terms of dockside amenities, living on a boat is like being in a little condo; no grass to mow, electric power, hot showers, appliances, fridge, all the goodies. However, your 'house' is trying to biodegrade a little more quickly than a normal home if you are sitting in salt-water, but anything you live in requires service, and you can't untie your condo and go poke around the islands for 2 weeks. If you are planning on going to the South Pacific, you're likely looking at either a sailboat, or a very efficient diesel trawler. There are tons of either of these of every type and description. Talk to lots of people and ask lots of questions before throwing your money into that hole in the water! Good luck!!