Before you start designing your system, I suggest that you use a
Kill-A-Watt meter to measure how much power your various loads actually use. The nameplate rating on most devices seems to be little more than a wild guess. For instance, you may find that the nominal 75W rating for a laptop computer actually averages out to 30W power use. Use it for 10 hours a day, and that's the difference between expecting to use 750 Watt-hours (and sizing the rest of your PV system to account for that load) and actually only needing to use 300 Watt-hours. You can use a DC clamp-on ammeter to measure your RV's 12VDC loads.
Next, look at conservation. The cheapest PV Watt-hour is the one you don't have to produce.
Once you have a handle on how many Watt-hours your loads will use in a day, then you can calculate battery bank capacity. Ideally, you'll cycle your battery bank down to about 25% depth of discharge (DOD) in routine use, with occasional dips to 50% DOD. It's not a good idea to oversize your battery bank, because that makes it too difficult to recharge it fully. Keep in mind that your inverter will also be a load for which you'll need to account. Taking your proposed 12V/675Ah battery bank down to 25% DOD would provide about 2000 Watt-hours of energy. That's a pretty hefty power requirement for a Class C RV; conservation could cut your requirements by half (or even more).
After sizing your battery bank, you're ready to calculate how large your PV array needs to be. Over at the
NAWS forum (where I also post as AuricTech), the rule of thumb is that you want somewhere around a 10% charge rate, assuming four hours of "good sun" on average. Since your panels will generally not produce their rated power, the folks at the NAWS forum tend to use a derating factor of .77 (i.e., multiply your PV array's rated Watts by .77 to estimate how much power your array will actually produce).
Assuming that you go ahead with your 12V/675Ah battery bank, here's how I would calculate the required PV array size to keep that battery bank properly charged:
(14.5 charging Volts * 675Ah battery bank * .10 charging rate) / .77 derating factor) = 978.75W PV array
As you can see, it all starts with a good calculation of loads....