WRT your question about whether or not a quilt would fit into a sewing machine, as others have said, a tightly rolled up quilt should fit into most standard machines but you can, if you pay a bit more get machines with a longer arm with are designed specifically with quilitng in mind.
On the other hand, if you want to quilt a whole quilt you are best off avoiding the budget or very lightweight, cheap machines because they may have a shorter than average arm.
You can get some very complicated very advanced machines but I would give those a miss personally. They are impossible to cart around so if you join a group or go to a class you have no hope of moving them. Plus there is more to go wrong. I also find that I have a fairly advanced machine with a lot of embroidery stitches for example, but I rarely, if ever use them. So long as you can vary the length of stitch and do a zigzag and maybe a button hole you are sorted.
1/4" feet seem to be a mixed blessing. Some love them, some don't but I think it partly depends on how accurate your machine is with them fitted. Mine seems to be spot on (Janome machine) but I know others aren't. I suspect it varies from machine to machine rather than by make. You can also get machines where you can fit the 1/4" as a guide on the foot plate which is helpful too.
Personally I think you need to try out a few machines but don't be distracted by the whistles and bells, just see if you like the way it is set up.