We also have a two story house with the lower level being a finished basement with a full apartment. We have wood stoves on both levels, so I can give you first hand information on the advantages/disadvantages of stove placement. As for heating, it is always going to be better to place the stove on the level where you plan to spend the most time and want to have the most comfortable temperatures. Moving heat from a basement stove is a challenge and often not successfully accomplished. Judging from the comments here at the forum I would say it is seldom accomplished at high levels of satisfaction.
If you end up being like many of us dedicated wood burners you will also want your stove to be placed so that you can enjoy experiencing the radiant heat coming off it as you sit and admire the flames. Again, this means to maximize your pleasure you will need to place the stove where you will have such access to it. A finished basement tripped out as a man cave can deliver this enjoyment, but in most instances it is more likely achieved when the stove is on the main level of the house.
Wood stoves are inherently messy. No way to get around it. I've found if you develop proper habits it is relatively easy to deal with the mess. I keep a cordless hand vac handy and always take a minute or two to police the stove area after a reload. You get a good feeling from seeing everything neat and tidy around the stove. And keeping the wife happy is a must for most wood burners, so tidying up is always a good start in accomplishing this vital goal. Removing ashes is going to put some dust in the air, even under the best of circumstances. If this is a big problem it's going to hard to get around with a stove in the living room, etc. Placed in the basement might eliminate the problem on a practical level if you aren't going to spend time in that area. Or, acquiring the habit of picking up a dust rag and dong a quick once over on the nearby surfaces is another way to deal with it. Just don't think your wife should do the dusting unless you want to get her dead set against heating with wood. Of course, if dust doesn't bother the people living in the house, then this won't be as big an issue.
Your basement wood storage idea has its pluses and minuses. Wood stored in large quantities inside the house can lead to higher humidity (especially in a damp basement), but if your wood is properly seasoned that problem can be minimized. Bugs are going to be in wood and thus inside your house when you store wood there, but if you are selective in harvesting and storing your wood supply you can minimize this, as well. For me, bringing wood to the stove for loading is all just a part of heating with wood and I don't think of it is an unpleasant chore. It is what it is and I enjoy burning enough I rarely think of it in a negative manner. I have a wood storage bin that I built that is right outside the sliding glass door off the dining room in the corner of our screened room, so I keep that topped off and I only have to carry a load of wood about 30 feet to the living room stove.
Tending to the fire is usually more work with a basement install if you are going to be upstairs most of the time. Establishing a fire can take time (on a cold start up it can run to an hour) and you really want to be nearby to monitor and control the air, etc. You can't just throw some wood into the stove, light it, and then go about your business. Having the stove across the room makes monitoring things much easier. The same is true with reloads. Looking up from your easy chair to see how things are going is much easier than running down the stairs to check on things.
Finally, how you will be running your chimney is a fairly big consideration. You will almost always have a shorter run on an upper level install and that can reduce your cost. If you are fortunate to have a straight shot up through the roof, even better. Basement installs are likely to be longer runs and cost more. Also many basement stoves seem to have trouble initiating a good draft, but that can usually be remedied with some trial and error. Moving the heat is a bigger problem than the draft in most instances with a basement installation.
Good luck with your choice.