You need to know where you're going before you plan for how to get there.
If you haven't done a complete load analysis, you can't have any idea of what you'll need in the end. Which means anything you do to get a 'temporary' system up & running is likely to be money down the drain. For someone on a budget (and aren't we all?), I don't feel that's the best way to stretch one's dollar.
Based on what you have said regarding your anticipated power needs, you'd be much better off with a 24V system. I'd start with that from the get-go. Do the wire gauge / voltage drop calculations on 12V @ 6000W (which would likely be around the peak surge voltage a 3000W inverter would provide). Most pros will tell you 12V systems should be limited to ~1000W. Doing the math quickly shows you why.
I alluded to it before, but I won't beat around the bush this time... a generator isn't just a nice thing to have with a solar system. It's a necessity. If I were you, honestly - I'd start with that FIRST. A nice small quiet unit that can be paralleled with a twin. It will power everything you need right now, sip fuel, and most important - will be just as useful no matter what system you come up with. The same can't be said for a 12V inverter (useless when you upgrade to 24), your panels (which would have to ran in series w/ a 24V system, which is not ideal from a shading perspective), or your battery bank (likely not going to transition well, if at all).
Finally, I wouldn't even consider lithium batteries when you're financially constrained, especially when they may not even have a place in your evolving system.
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