I am currently stationed at Fort Drum, maybe an hour from Oswego. Oswego is a gorgeous mid-sized town (a big town for northern New York). The nearest large town will be Syracuse, perhaps 30 minutes from where you are. It's right by Lake Ontario, so you'll have gorgeous views depending on where you decide to buy a house. The town has a very long history, it used to be a manufacturing town but from what I remember of my visits there most of the manufacturers have left.
I would suggest making sure you own a 4WD vehicle, or at least a car that can handle a lot of snow, because you're going to get hit by the very worst of Lake Effect snow, which is NOT a joke up here. Ten foot blizzards are not uncommon, and you'll see snowplow drifts 30 - 40 feet high after a good one hits. I had an Escape when I was first stationed here, and although I switched to a smaller vehicle later, I miss that SUV like fire in the winters. Have an emergency kit in your car, to include blankets and warm clothing.
As for housing, look for something built between 1950 and 2000, those are the best-built. Expect that you will have to upgrade the insulation and probably the heating systems. That's normal across the North Country. Also, electricity rates go up in winter because National Grid has an effective monopoly up here. I suggest getting on their rate plan so you can spread the payments out; it's not uncommon for your electric bill to be at least $200 a month in winter, depending on your housing insulation and heating type. Many people have woodstoves in the area, and many others rely on gas. I can't speak to wood costs, but gas is also very expensive, as is oil. You will find that how you choose your house and how you renovate that house will be dictated almost entirely by what it will be like in winter. Be prepared for that.
Gasoline costs in Oswego are probably slightly less expensive than near Drum only because the pipeline ends near Syracuse, so all of our gasoline gets trucked in; you're closer to Syracuse, so the cost will be a few cents cheaper, but the average cost in winter hovers around $4/gal. They use salt on the roads here, not sand, so expect higher costs in vehicle maintenance to wash the salt off periodically and treat car parts affected by its corrosion.
That said, I am hard pressed to think of a more beautiful section of the country than Northern New York (the sole exception would be Vermont, and I am partial to Vermont). Take every advantage of Oswego's location near Lake Ontario and the ADK; travel as much as you can. The autumn is breathtaking. Syracuse has hundreds of stores and a huge mall, if shopping and restaurants are your thing. The finger lakes and the Adirondack park are all within easy reach; with them are parks, museums, wineries, you name it. If there is an outdoor activity that you can think of, you can do it up here. I'm going to miss this area like crazy when I leave, and I'll always ask to PCS back here in future. Canada is an hour away; Montreal is three hours from Oswego, Boston 5 hours, NYC 6 hours. Oswego is an excellent place to live, regardless of where you work within an hour radius of the town.