When I first purchased the RV, I swapped out the factory installed coach batteries for a set of 2 12V 100AH batteries running in parallel
Get those 4*6 if there is enough room, but this is not crucial if your energy needs are what you said. 2*100 AH will do.
I'd be interested in installing one to use for charging laptops, cell phones, and occasionally watching TV. What size inverter would you recommend for the battery setup and for the use that I am looking for?
200W inverter, and this doesn't change if you add more batteries. $25 modified sine like 175W GoPower will do for laptops and phones, it "might" work with TV or might not. Some TV prefer Pure Sine inverters, those cost more.
Is an inverter installation pretty straight forward and can someone with little electrical experience do this on their own?
For 200-300W inverter, - yes. Just run any wire that you have in your shed. A few old lamp cords spliced together to make 15-20ft run from battery to inverter. Place inverter near TV and tuck that lamp cord so that you won't trip over it. Without basic electricity knowledge I wouldn't do anything else like wiring inverter output into 120V receptacles of the trailer etc.
I'd also be interested in using solar power for charging the batteries. My main concern would be installing panels on the roof and causing potential leaks, wind resistance, etc.
Your worries are misplaced. There is no concern with wind resistance on flat panels (not tilted). There is no concern with leaks with #10 screws in 3/4" particle board of the roof. Just use stainless screws and plenty of Dicor sealant under the mounting brackets and on the screw heads.
Since we tend to boondock in an area for about a week at time, as long as our water/tanks last, I wouldn't mind having portable solar
With your minimalist use you need at least 180W solar if it's mostly sunny and 400W if it's not. (There is also a rule to oversize the solar by 30-50% from what you think you need, this has been proven by thousands users). You will run several other devices that you didn't mention - pumps, lights, 12V circuit of propane fridge, possibly furnace. Portable "suitcases" are 100-120W max, as I recall, and it will be more expensive per watt than roof-mounted. Portable could be beneficial in partially shaded areas though. When parked in dense leafy shade, solar power is reduced several times.
portable solar panels that I attach directly to the battery to charge
You don't attach any panel bigger than 15-20W "to the battery directly". Portable suitcases include solar controller that is wired between the panel and battery. If you buy panels for roof install, there are also kits that include the controller (check Solar Blvd), or you can buy controller separately (that would be my preference).
PS: there has been a tendency to post "solar" questions in Tech section, rather than DIY.
