Some cold weather--Apple trees have what is known as a chilling requirement--this means that they need some cold weather in order know when they are supposed to lose their leaves, bloom and perform other milestone annual events. If you live in one of the 40 or so US states that "have winter" your apple tree's chilling requirements (often about 800 hours of temperatures below 45oF) will be met. However, if you live in a very warm area, such as Central or South FL or most parts of other Southern US states, your apple trees will most likely never bear fruit: maybe you can grow citrus instead!
A large, sunny spot to plant your tree in-- If you are going to grow your trees in a relatively "natural" shape, as opposed to trellising or espaliering them, you will need a fairly large area to grow them in. If you don't have much garden space, or if you have a fear of ladders and heights, you should grow a dwarf apple tree. A dwarf tree will be shorter than 10 feet tall when it is full-grown and won't require very much space--about 40 square feet would be adequate. However, like all apple trees, they will require plenty of sun (full sun is best), and relatively fertile soil. Semi-dwarf and standard-sized apple trees will require up to 300 square feet of space to stretch out in.
Keep in mind that you will need to plant at least two different varieties of apple tree that bloom at the at the same time in order to ensure that your tree's flowers get pollinated, so make sure that you have enough space for at least two trees.
Suitable varieties of apple trees for organic gardening
Sustainable and organic apple growers should plant a disease-resistant tree that is going to be small (or big) enough to fit their space and equipment (a big tree calls for a big ladder) constraints. Keep chilling requirements in mind when selecting your tree--if you plant a variety with a low chilling requirement in an area that has long, cold winters, you your tree may be apple-less most years because its blooms consistently get frosted.
The ability and willingness to give your trees consistent, year-round care-- In most parts of the country, organic apple trees will require frequent disease and pest monitoring. Unfair, but true: those of us who live East of the Mississippi River will have to do a lot more of this than our Western neighbors. Eastern organic growers will probably have to count on spraying their trees (with organically-acceptable materials such as Sulfur to prevent fungus and Kaolin clay to reduce insect damage) at least a few times a year. All apple trees should be pruned at least once a year (in winter), fertilized twice a year, and staked or trained as needed.
Patience and Acceptance--These are qualities that are as useful for apple growing as they are for just about anything else: your tree will take several years to bear fruit, and when it finally does so, it will probably be smaller and less cosmetically perfect that "grocery store fruit". However, its taste and freshness will be beyond compare, so you will be rewarded if you can overlook your apple's imperfections.
Growing you own organic apples can be somewhat time consuming, but once you get the hand of managing your trees, it will be very rewarding as well.