Good morning, and welcome.
I can empathize--my house didn't seem well set-up for a woodstove, either. Was forced to think a lot through before the first hole was cut, and it worked out well in the end. Expect uncertainty and a few mental dead-ends while you're going through the process, but know that it's worth it in the end--hang in there.
Yes, a wood stove can do what you want it to do, and very well. You're wise to start with a fresh install, leaving the oil burner in the basement intact for those times when you need to travel/get sick/have a busy schedule/have a wood shortage. Options are wonderful to have. You're also wise to put the stove up on the first floor instead of the basement, for many reasons. We have folks here who try the basement and end up moving the stove upstairs (others who leave it--so it works for some).
Yes, you can get even heat throughout the house--that's as much a factor of insulation and circulation as the stove. You're working on that--very good. I think you'll be pleasantly surprised at how level and even heat can be throughout a house with a woodstove. I too feared the hot-spot/cold-corner outcome, thought I was just getting a space heater and would be happy with any warmth to corners I got. Instead, I ended up with whole-house heat from a modest-sized parlor stove in a 2000sf house in the middle of Alaska. You shouldn't need a huge stove for what you have--medium-sized stove, great chimney system, and put the extra money into insulation. Locating your stove with at least the back of it in the under-loft area will help move heat over instead of all going up if you have open ceilings in front of the loft.
Some folks love their pellet stove. Twenty minutes in a showroom listening to one run confirmed my idea that I did not want one. I also wanted the independence that wood gave me--in case the boiler went out, in case the power failed, in case the price of oil went through the roof. This was my first winter with the stove in this house, and my boiler, in fact, did fail, and then we had some mighty storms and the power went out, too. And now it looks like oil will be going through the roof again. My wood stove just keeps cranking away and keeping me happy. Your call--but just think through all the reasons you want another heat source and you'll end up knowing what you want.
Agree with Dennis that soapstone would be a good choice given what you've described, and that the folks in Lebanon are top-notch and build a great stove. I'm happy with my Hearthstone, but had actually made the decision to go with a Fireview at first, but it didn't work with my configuration. I love the big window and the great flickering blue flames of the Hearthstone, and the simple lines of the Hearthstone worked better in my house than the more ornate, Victorian look of the Fireview. A non-cat stove is also a better choice for me because I have teenthings (and their friends) operating the stove as well as me, and the attention span of a teener can be amazingly short. I'm learning to speak in very short sentences with them, using words of one syllable or less. I think cats are great, and that wasn't really a factor for me in consideration, but only because I didn't think that part through. Got lucky.
Recommend you start getting firewood for next year, and the next, asap. Also start thinking about how you're going to store it--consider a woodshed project this summer if you don't already have storage taken care of. Site the shed as a windbreak if you can--killing two stones with one bird. Or plant some trees that will help with that. Think things through about where you're going to store the day-or-two pile inside the house, which entry you'll use, how you'll get the ash out, etc.
A sketch/detailed description of your house would help us give unasked-for advice about location, circulation, etc. It's how we keep ourselves amused. Important info: ceiling heights, windows, orientation to sun, is plumbing centrally-located, or on outside walls?
Wild thought: you may end up deciding to go with two wood stoves--a middlin' sized one centrally located, and a cute little back-door stove or dining room stove to take the chill off the far end of the house. Although folks used to do it all the time (google `four-o'clock stoves for examples), stoves in bedrooms are not advised. But there may be another location where you can have a little Squirrel stove or a a marine stove, or some other backup stove like that. Just don't put it on the `no-way' list yet. Know that it's an option. Wood stoves get addicting--I'm kind of disappointed that I don't need two. But not everyone is wired like that.