Before buying a battery, I'd recommend that you read Gary Brinck's article about RV batteries in the Forum library. I think it will help you decide which type/size of battery would be best for your needs. If you're only going to get one battery, I'd recommend a true deep-cycle battery with at least a 100 AH rating - not a marine-type battery. Car part stores often sell, so-called, "deep cycle" batteries and they usually don't last very long. They've often got an AH rating of about 75 to 85 amps.
Let's assume you get a 100 AH battery and your RV is NOT shaded during most of the day (that's important). If you were to install a 100 watt solar panel, they're typically rated to generate about 5 to 6 amps of power each hour. The solar industry uses 5 to 6 hours as an average for how many hours per day a solar panel can generate electricity. So under IDEAL conditions, that 100 watt panel would generate about 30 to 35 amps per day. Now... in reality, a 100 watt panel is actually going to be able to put no more than about 4 amps into your battery-bank each hour - on a good day, in direct sunlight. That's due to wire-run, wire thickness, solar angle, installation errors etc.
Your usage requirements are somewhat different than most off-grid RVers. Most want their solar systems to replenish as much of their daily power usage as possible, but you said you're only going to be using your RV one day each week and the remainder of the time there will be little (if any) power use. For the "typcial" RVer with "typical" power usage and a single 100 watt panel, I usually recommend that they NOT buy/install a solar charge controller, because a single 100 panel won't be able to replenish all the power they consume in a day. There's no chance that a single 100 watt panel could overcharge/damage their battery bank. In your case, however, I would recommend that you buy an inexpensive PWM charge controller. Since your RV won't be used during most of the week, which means it will have little, if any, power draw, and since you'll only have one battery, a single 100 watt solar panel could overcharge that battery - especially if the battery wasn't low to begin with and the solar panel was in direct sunlight. An inexpensive PWM charge controller will prevent overcharging.
Now, if your RV is shaded during most of the day, that will have a significant impact on how much power a solar panel can generate. Only you know how much shading your RV has. In that case, if you still want to move forward with solar, I would recommend that you buy a single 100 watt panel with a PWM controller (you can get panels and controllers in kits), and see how well it keeps your battery topped off. You may find that you need to install additional panels to overcome the shading affect, but a PWM controller, rated at 20 to 30 amps, will allow you to expand your system safely up to about 300 watts. Beyond that, you'd better be looking at an MPPT controller - more expensive but more capable. With a single battery, I don't see you needing an MPPT controller.
Good luck.
Kev