Tandi:
First off . . . welcome to hearth.com. This is a good site with good people who want to see you succeed in your wood burning endeavors. Sometimes we can be cantankerous, sometimes we may seem a bit rough . . . but at the end of the thread, most folks simply want to help others burn safely and stay warm in the winter while burning wood.
To answer your questions . . . and to reiterate some key points made by others.
I would be a bit leery to just unhook your oil furnace. 1) Your insurance company may (or may not) have a problem if your home is heated solely by wood. This is something you should check into before yanking anything out. 2) $@#% happens . . . maybe the seasoned wood you get the first year is not seasoned enough, maybe the Polar Vortex hits and you discover the woodstove just isn't up to the task of heating the home, maybe you get sick and cannot tend the woodstove or you have an emergency out of town and have to leave the house unattended . . . trust me . . . while I predominantly heat with wood . . . it's really nice to have a "conventional" back up source of heat. If you end up not needing to burn a drop of oil -- fantastic -- but it's far better to have that back up heat source in place and not need it versus discovering you need a back up heat source and you don't have it ready to go.
I may have missed it . . . but where are you placing your new woodstove? Around here most oil furnaces are in the basement or in an utility room. If you were hoping to simply pull the oil furnace pipe out and connect up the woodstove you may be less than happy if the woodstove is situated in an uninsulated or unused basement . . . or if it's located in an utility room and not in the main living space. Yes, putting in an additional chimney (around here most folks seem to prefer Class A -- a stainless steel chimney) will be an additional cost . . . but a) you'll know the chimney is good and ready to go (which may or may not be the case with using the existing chimney) and you will have a lot more options as to where to put the woodstove. Me . . . I like having the woodstove where I spend most of my time -- I get the full benefit of the heat plus, you'll always know when you need to reload and you get to see the fire which can be as entertaining as many TV shows.
You've pretty much nailed down the steps to processing wood . . . but you may have missed a few steps depending on how you get your wood. If you're cutting down a tree on your property (in my opinion one of the more dangerous aspects when it comes to processing wood) you need to cut down the tree with a chainsaw (and there is a definite learning curve here), de-limb the tree and then buck it into stove-length pieces (which vary according to the size of the stove's firebox.) After that you need to split the wood (splitting ax, maul or splitter -- rental or owned) and then stack the wood (getting it off the ground) . . . and then wait . . . generally folks will give most wood species 9-12 months at a minimum before burning . . . some species, such as oak, need a few more months typically.
As for the cheapest way to get fuel . . .
1. Finding free, cut and split firewood on Craigslist or from a friend who may be moving or is no longer burning wood (Without a doubt the cheapest, but also about as common as spotting the elusive rainbow colored unicorn of Atlantis).
2. Scrounging wood that may or may not be bucked up from neighbors, tree service, Craigslist, asking about wood you see on property beside the road, etc. (This often seems to be a feast or famine deal -- some folks make out like Fat Cats with fantastic hauls of primo hardwood . . . sometimes delivered right to the house, while in other areas folks really have to work to find anything and even then it may be slim pickings in terms of what you find.)
3. Slabwood. This is another hit or miss deal. In my neck of the woods, just about every single sawmill only cuts softwood and the slabs are usually pretty thin. If I can get some free slabs to use for the shoulder season or to make kindling I'll grab some . . . but I don't go out of my way for it. Now, that said, across the river in Eddington at Peavey Manufacturing (where they still make Peaveys) folks can buy white ash remnants for a pretty low price (but to be honest from what I've seen most of this is pretty small stuff and not worth my time or cash.) In some areas however, sawmills are cutting hardwood and some of the pics of the slabs have been pretty meaty. Sometimes there is a charge . . . but oftentimes the charge is pretty low compared to buying pre-cut firewood. An advantage is that slabwood due to the size can season pretty quickly.
4. Tree length wood. If you have to buy wood and you're willing to work a little harder this tends to be the best deal. Wood will be delivered in tree length so you will need to cut it, split it and stack it. It's more work, but can be as much as half the cost of firewood that is already bucked and split and delivered to you.
Your stove needs well seasoned wood. If you haven't bought wood by now you really should . . . if you plan to burn wood this year. Be aware that "seasoned" wood means different things to different folks. A seller may consider seasoned wood that he cut down six months ago and has left in tree length . . . whereas many of us here consider seasoned wood to be wood that is below a certain moisture level. It can a challenge to find truly seasoned wood. Generally, the earlier you get your wood, the better off you will be . . . even better is to get wood a full year before you intend to burn so you will know your wood will be ready to go.
Final thought . . . if you have other questions ask away . . . this site is here so folks can learn . . . and you only learn by asking questions . . . well, that's not quite true . . . if you do a whole lot of reading here you can learn a lot as well.
Again, welcome to hearth.com.