Your garden is large enough for a tree unless you have lots of flower beds, veggie plots, play areas etc. There are now many apple trees available that don't grow very large at all. Try a fruit tree nursery and ask their advice.

remember you will need a pollinator
some trees are called family trees with two or three varieties grafted onto the same rootstock and they pollinate each other also you can have eaters and cookers on the same tree-- ideal if you only want one

if you get one grafted on to an m9 root stock, that will with proper pruning stay at about 9feet high, but if you are only having one get a self polanater, unless there is a crabapple tree close by, if you mention what I have said to your local garden center they will know just what you want but tell them also that you want either a desert or a cooking apple , you have got untill march unless the ground is frozen, you can get pruning instructions from the site ,you only have to ask,

If you are brave and don't mind a project, you can grow an apple as an espallier - that is trained against a fence in a fan shape or horizontally trained braches. I've even seen them grown along to form what I can only describ as a long railing, only about 2ft off the ground. I could try and explain how its done, but it's hard without illustrations, so I suggest a visit to your library and they'll have plenty of books about this.