I am near Albany, NY and I can relate to your battle. Here is my take:
I started trying to do the same thing with about the same budget. If you do not have building experience (as you stated earlier), I would consider get a very large shed. That is what I was going to do instead of building my garage and I think it would have worked reasonably well. I started with idea of 12 x 20 shed, then moved up to a 14 x 24, then up to the biggest they can sell and run on the open road in this area... 14 x 32. Here is the good part about a shed, you are not on the cold concrete. It's really easy to get (order it, prep the site with stone or as they instruct and wait for it to show up). When it's ready they just drop it on your yard and BAM intant garage. I priced out the big daddy at around $7000 - $7500. You can custom build them any way you want, so you can add head room or attic/loft space, etc. Just make sure they know when they build it to double up underneath the floor and the flooring material because you are going to put a car in it.
With that said, if you need more room, you can definitely do better if you build it yourself. I got way more than that and I am way happier. But I had to save and sell some things to make it happen. The shed thing is very limited, but if it is all you can handle.... it's an option for you.
Another option, do you have any Amish builders in your area? I have heard some really good prices for good sized pole barns and buildings from them. Your biggest obstacle is going to be the fact that you don't have a lot of experience. I think if you can't get the Amish, I would suggest what others have and get the pole barn to start and pour a slab in it later.