Suggest you send for Pomona Fruits catalogue. (Or look on line for them)It shows you the various heights and which need pollinators or don't need them and lists varieties that are not often met with as well.. There are hints on flavour for some of them too. If you have a neighbour with a crab apple you may find that will work as a pollinator too - depends greatly on exactly their flowering period coinciding.
If you fancy a cooker try Lord Derby - wonderful flavour!

AS Steragram suggests, Pomona have a good lot of information, as do Blackmoor and many others

Reagrding pollination, again as above, may not be a problem if neighbours also have apples

Becuse it will be your only tree may i suggest the variety is not one readily availabe in shops?

One that is self fertile & never in shops because it just doesn't travel or keep well, but still a great apple, is James Grieve

Its a personal thing but James is not one of my favourites. There is one called Christmas Pippin, similar to Cox but easier to grow (but if you have a pot grown one you probably won't have enough to save until Christmas anyway!) But Pomona's catalogue (I haven't looked at the others) gives you lots of notes re flavour, keeping etc. Or you may take the opportunity of trying one you don't usually see in the shop.
If you want a cooker Lord Langbourne beats Bramley into a cocked hat for flavour!

I've not tasted Christmas Pippin but whne I was looking for something similar I came across Pinova, which is cross between Cox & Golden delicous with a few others bunged in

I have it in a pot, growing for 3 years now and this 3rd year it is settling down well and I've just picked the crop

The taste is one I'd call complex, not sweet, not sharp but very nice

Says it keeps until April but as SG says, one tree will not last until Christmas

https://www.blackmoor.co.uk/products/636

Oh dear, mind wandering again - Lord Lambourne s a dessert apple not a cooker, and I didn't even spell it properly. The one I was trying to recommend is Lord Derby - I knew it was one of the aristocracy... Sorry