It's cold up there in the north country. The normal gardening season is about 75 days in a good year and seemingly about 45 days most of the time. I figured out, early on, that there wasn't going to be any way I'd be able to afford to buy fuel for heating if I planned on staying comfortable. Fortunately, I'd had the foresight to purchase a Stihl chainsaw before moving north. If you're ever in the market for an excellent woodcutting tool - I recommend the Stihl saws highly.
For the 10 years I lived up there I heated solely with wood for 7 of those years. I burned an average of 9 to 10 full cords of hardwood each heating season which was all cut, split, stacked, and carried by me. That's a lot of work but there are few chores that I looked forward to more than making wood.
I was located in an area that was adjacent to thousands of acres of county owned timberland and great portions of it were regularly logged for pulp (mostly the popple and pine). By getting a permit from the local forester, I was able to go into the cut-overs after the loggers were done working for the day and pick up all the wood that they weren't planning on trucking to the pulp mills. That meant that anything under about 6" diameter was there for the taking. The loggers, while cutting mostly pulp wood, also took a lot of oak and maple for lumber - sorting it to different stacks than the pulp logs. All the tops and anything less than lumber size or lumber quality was left behind for the picking. Pulling tops apart is tough work in the late spring when the black flies and mosquitoes are about... hot and tiring, but there's plenty of wonderful fuel in there!
I could get about 1/2 cord (a cord is a stack of logs 8 feet long, 4 feet wide, and 4 feet high: 128 cubic feet - what is generally sold as a cord these days is a 4'x 4' stack of 14" or 16" logs - what used to be called a face cord) into my truck, so there were lots of trips down those sand roads to pull out the best of the leavings. I only picked up the maple and red oak for the winter heating, though I occasionally picked up some solid birch for the fall and spring fires where not as much heat was required and some red pine to split down to kindling size.
The toughest part of getting in the wood is finding the time to let it season. You can tell a stack of well seasoned wood by looking at the ends of the logs that've been stacked. If the grain on the end of the logs is 'checked', it's ready for the woodstove. You'll be able to see when it burns if it was properly dried, too; wood not thoroughly dried will sizzle and pop and smoke an awful lot. Good dry wood burns clean down to a fine ash and minimizes the creosote buildup in your chimney.
Red Oak is the woodburner's delight. It cuts nicely, spits easily, stores well, and burns with a high heat output. Save some of the nicer sticks you come across and slab them out into boards - working with hand-made lumber during the long winter months is a treat, and what would make better Christmas presents than nicely dovetailed little boxes that you can make for your loved ones from logs out of the woodpile? If you've got access to red oak, count your blessings. You'll be warm.
There's a lot of maple up in the northwoods, too, and it is also a great source of fuel. Nice to work with, but occasionally a bitch to split. Once dried, it burns wonderful and fragrant. Try splitting it after a good freeze - it'll most likely just pop apart then.
If you're in an area where there's a lot of birch that you have access to, be sure to cut it up and split it as soon as you're able... left as solid logs inside that water tight bark the wood tends to rot quickly. Nothing is prettier than a couple of white birch logs in the fireplace and, if you split it up while it's still relatively green, the bark will just pop off. Stack that bark up out of the weather and you'll have some of the world's finest kindling for those cold and blustery mornings.
A couple of pine logs will be plenty if you have access to the more desireable hard woods. It's nice to have some pine around to split down to kindling size as it lights easily and burns fast. Pine will crap up your chimney a lot quicker than the hard woods will. It sure does smell good, though, when it's burning, and in an open fireplace it's as picturesque as birch logs. Pine will rot more quickly in the woodpile if it's not well protected from the weather.
If all you've got is popple (aspen), be prepared to spend a lot of time carrying wood - more carrying time than there'll be sitting-in-front-of-the-woodstove-with-your-feet-propped-up time. It burns fast and clean, doesn't give off a heck of a lot of heat, and makes a prodigious amount of ash. This, too, is worth throwing in the kindling box. Keep some sticks of popple around for carving or whittling. I've seen a guy that dragged a portable band-saw mill into a nice popple stand, cut it all to 1" boards, and after drying for a little better than a year, had it all planed down and paneled his kitchen with it. It was beautiful.
Ironwood grows around the north country - Hop Hornbeam, I believe is the alternative name. So dense that a log of it won't float, an absolute bear to cut, and nearly impossible to split. Once you've got it nicely dried, though, a couple of sticks tossed into a well established fire will last through the night and give you a great bed of coals to kick up the morning fire. I used ironwood, when I could get it (sometimes that entailed hours of hiking in and dragging sticks out), to make wedges for splitting. They last for years and stand up well to the abuse received around the splitting shed.