It all depends on your intended use. Battery banks require maintenance, have a definite life expectancy of only a few years, will require some fabrication, and will cost some money. Generators, on the other hand, have a pretty high initial expense and continued operating costs (gas, oil), but will likely hold some value whereas a depreciated battery bank is...well...lead scrap.
Here's the thing though. Without an inverter system you won't be able to run 120 volt appliances without the generator running or shore power hooked up. Period. I can't imagine doing that. When I go to a campground I pay the extra couple bucks for electrical hookups. However, going down the road I run on my batteries utilizing the alternator to keep things charged. When I stop for a short period of time I use my batteries to keep my fridge going. When it's late at night and I'm boondocking out in the woods or where ever I run off my batteries. It would be a serious pain to have to leave the generator running all night. On the other hand, I don't like stumbling around trying to get out to take a 4:00 am pee.
Only you can decide what to do, but realistically I think a battery bank would be the first thing I would set up if funding was tight. There is always shorepower at campgrounds. I also have a generator for 120 volt AC power, but I rarely use it. Heck, I use battery power and my mowernator to recharge the batteries far more frequently than the generator if I don't have shore power available. But you also have to balance out your load requirements as well. Your 3000 watt estimate seems high to me, but is well within the realm of possibility. Are you trying to run AC off battery power? Is there anywhere you can cut back? Life on the road requires some adjustments from what we're used to at home.