I've put in a few solar systems while in AK...trust me, buy the biggest you can afford and buy a system you can add on to. It's worse then building a shop, never big enough. Save the money from propane and go with a renewable source. You have plenty of available roof and a big family. Go for broke!
Short of any other words and being the honest asshole I am, you'd be a damn fool to put in a tiny system. Make it comfortable for the kids so they effin LOVE going! You know they're gonna want to charge their smart phones and such. A small fan on that wood burner would be nice as well. Add a boot drier and a small radio...the list is endless bub. Don't be a fool. You got a hell of a cabin going. Personally I'd put off finishing the inside for a power system this year. But that's just me, it's your money, this is just my honest opinion.