Why don't you just buy yourself a nice premium lemon tree for starters (and skip meyer lemon) and take care of that. Four winds sells nice trees. If you speak to a customer rep. they may even separately sell you a rootstock to play with. You can get trifoliate seedlings cheap on Etsy. One green world uses rubidoux trifoliate and would likely sell you one with a purchase. Scions are another matter. As far as multi grafted trees I'm not a fan, had 4 in one pears etc., multiple issues and thats with a year round outside tree not an in/out tree.

Not necessarily trying to discourage you from grafting, but you might consider just growing individual trees for now. See how they do in your particular winter quarters. If your basement is really warm, they may be plagued with bugs or not grow well. And it can be difficult enough to get one variety to grow and fruit well, let alone a tree with multiple varieties.

Grafting, in my limited experience, is best done in summer when plants are actively growing outdoors. But having multiple varieties on one tree can be tricky because they all grow at different rates and one variety may take over. I'd consider grafting if a particular variety was difficult to obtain and I had access to scions through the mail. There are tons of citrus grafting videos on YouTube. But I think they don't always tell you the best time of year.

Your goal seems to be to get fruit, so I think you'd be the most successful with growing individual plants, for now. If you have tons of success, then venture into a 'fruit cocktail' type of multi-grafted tree.

For cooking, consider key lime (love my key lime pie!) , lemon, and Persian lime. For eating out of hand, I like and have had success with any early-bearing mandarin/satsuma. I'm also hoping the Oroblanco is good. It's a sweet, acid-less pummelo-grapefruit hybrid (my plant is still young though). Oranges and grapefruit I can get in the store.

The main reason I want to graft multiple trees is just for space. One is manageable in my limited space

Anything in a pot will have enough problems as a single cultivar. 2 in 1 tree will not grow.

i would probably keep similar types together. For instance I have a lemon tree that i grafted limes and key limes onto. Id give it to you if you anywhere near here, since im running out of room lol. But i think if you try too many different varieties together one type may become too dominant and shade out the other types.