What a great idea and a great topic !!!!! There has been some good information posted already.
If I wanted some specific apple variety growing, I would graft pieces of this specific variety on to any old apple tree that I could get to grow in my area.
So you could plant any old apple tree to get the basic tree established...then graft the varieties you want on to these trees later. These host trees would be called the 'stock' in some books. Grafting is generally done around the time when the buds on the host plant are starting to swell toward springtime.
The wood you graft on to the tree (the 'scions' or cuttings) should be cut from the known variety in winter after the leaves have dropped. I store them in my fridge wrapped in a wet paper towel...stored in a plastic bag. I might occasionally inspect them and sprinkle a bit more water on them. In the old days they just used to jam the cuttings into the cold ground in the shade somewhere. I understand the best cuttings are wood that grew last season....ie...it is the newest growth on the tree and will be the terminal shoots on a branch. I cut the graft wood up to a foot long then cut a smaller length later to do the actual graft. That way the ends can dry out and maybe leave the rest with some good life-sustaining moisture inside. I think they say that you should have maybe 3 buds on a good bit of graft wood. Growth starts at the bud, and if you did a good job you might get away with using wood that had only one bud if you were pushed.
I learned grafting from books, but it would be good to find an expert to show you.
I tie the grafts in place with a couple of turns of electricians plastic tape. I seal the cuts with petroleum jelly, or maybe acrylic house paint. You can buy special grafting tape and sealing wax/paste.
The critical thing with grafting is to keep as much of the cambium layer of the stock and scion in close contact as you can. Having said that, I've found you can get away with very little contact and the graft will 'take' and the cuts heal.
I've had a lot of success grafting apples. I have quite a few different varieties growing around home that have been grafted. I'm particularly interested in types that keep well and that are disease resistant.
Gotta have a good, sharp knife to do grafting work. I often might use an old slim-bladed slip-joint folder that used to belong to my uncle. This is one time where something small is better than the big choppers.
So the first step is to maybe look to see if you have any wild apples in the area already that you can graft to. Failing that you could transplant any old seedling that you find anywhere. I believe that the best results will occur if you transplant apple trees when they are dormant after the leaves have dropped. Smaller trees are more likely to 'take' than very big trees...but anything is worth a try. If you've got plenty of time you could imitate Johnny Appleseed and plant seeds....but you'd need to plant plenty of them if you weren't going to specially treat them to help the germination (although the climate in your area may be very favorable to planting apple seed).
Here is a graft I did at home maybe two or three months ago. It is doing well. I've grafted the old variety 'court pendu plat' on to a tree that is mainly 'fairbelle':
Here is a primitive graft used to join a desirable prune plum scion on to a wild plum root stock (or whatever it was). As you may notice, the graft wood is not lined up with the cambium layer on the root stock on the side you can see....but it was carefully lined up on the side of the sapling that you can't see in the photo. I think I did this graft two seasons ago. All I did here was to cut the rootstock plant off at about six inches above the ground and split it with a knife. I then cut a long tapered wedge on the base of the scion wood and pushed it into the split rootstock. I then applied a sealant to the wound area. In the old days the sealant might have been nothing more than a mix based on wet clay, or maybe animal fat.
Apple trees can really only be grafted successfully on to other apple trees. New grafted wood needs to be protected from being pulled at by animals.
Most rapid growth occurs on the highest points of the tree/branch. You need to make sure that the shoots of the original tree dont overtake the new graft. These may release hormones which suppress the graft growth. I am fairly brutal with trimming back the old growth. Grafts on trimmed-back more mature trees can grow at a surprisingly fast rate. You have to make sure that these more vigorous branches don't grow beyond the point where the graft joint can hold them. It will be a few seasons before there is much strength in the join.
What a worthy idea. Planting trees is a wonderful thing to do. Best wishes with the project