I can't recommend a tree type and I don't know anything about super dwarf pot apple trees, but whatever tree type you get you need to check out it's pollination needs. There's no point getting a tree if it won't produce fruit (looking at you Discovery
). Also you need to check out you have space for your tree or trees. Your looking at 4x4, height and spread for a small apple tree.
Some trees are self fertile but usually do better with a pollination partner, others need a pollination partner (definitely consider full grown space requirements). Apple trees are graded as being in a pollination group. They need trees in the same pollination group or to one pollination group above/below to get pollinated, other's are essentially sterile and won't pollinate another tree. Some trees need two trees of different types to be pollinated (triploid).
The Bramley I would like and the Discovery the Husband owns are in pollination group 3 and additionally triploid and cannot self pollinate. So we've one apple off a 7 year old tree as there's nothing nearby in the same group to pollinate it. We need to get two other trees to get the Discovery to fruit.
We're going to get 2 crab apples and a Bramley 20, crab apples are great for pollinating any other apple tree. The 2 crab apples are to pollinate and the Bramley (pollination group 3) to be pollinated as it won't pollinate anyone else. Just like the Discovery. Both Bramley / Bramley clone 20 need two other trees in pollination group 3 or 2 and 4 to produce fruit so I may as well take advantage of that extra pollen and get another tree in. The crab apples we've picked are Butterball (pollination group 3) which is high yield, resistant to scab and has a AGM (RHS Award gardening merit ). And Jelly King or Red sentinel (group 4) which has high yield, long lasting fruit.
I can't personally recommend but Bramley is known to be a great cooking apple. Bramley Clone 20 is a smaller version but very high yielding. I don't plan on getting super dwarfing rootstock.
I plan on getting bare root stock and planting in the ground so that it'll achieve it's full potential. You need a big pot to contain a tree and it's a lot of trouble to pot one up as it grows. It's also cheaper buying bare root and James Wong reported RHS findings that to get your tree to establish quicker your best to wash your roots bare, so why get pot grown? RHS found that unless you break up the root ball or wash off the compost the roots will spiral around it's compost ball and become pot bound while in the ground. The compost is more fertile than the soil so it'll keep it's roots in there. This stunts it's growth, limit's it's life span and makes it easier to fall over. If you wash the compost off a pot grown tree it'll prevent them from wanting to stay in it's lovely compost, making it get out there and make friends with the mycorrhizal fungi that helps trees thrive.
Husband (He who can do heavy work) will be soaking the tree in water for a few hours before planting, digging a big hole, mixing in manure, sprinkling the bottom with slow release fruit feed, chicken pellets and Root Grow. The latter is Granular mycorrhizal fungi which helps the tree produce roots and the fungi root network to help it thrive faster. Putting in too much manure below can cause sinking in the soil level so apparently it's better to put manure above the roots. Tree in, spread out the roots nicely, get your fancy decorative self going. Fill in with manure and soil mixture, tread down. Then lots of mulch and a load of water. Steak it in place as well. that's important.
Can you get a cutting off your Nan's apple? You can buy root stock and could try your hand at adding your cutting to a root stock.
I should point out I've done more reading than gardening. I'm all set for November's tree buying.
Edit to add, apple tree synopsis here from the site owner's book. Their brilliant books.
https://www.allotment-garden.org/store/fruit-nut-tree/fruit-apple