I use a Q Snap as well, a 12" x 17" rectangle. This is just the right size for me to sit in my recliner or on the couch and stitch away. I have quilted many queen and king sized quilts this way - though I had to teach myself to machine quilt to speed up the process on most of my quilting, I just don't have time to hand quilt all of my quilts.

I have a stand that has a clamp for the quilting hoop I have a large one I think it is about 18" but the clamp lets you change to different size hoops. for doing just a quilt block I just use a smaller quilt hoop and prop it up against a table.

Where to find
 

I am interested in trying the Aunt Becky. Where could I purchase one?

Another vote for a 11" x 17" Q-snap. Much better behaved than round hoops, especially in terms of shape, area covered, and ease of putting it on and adjusting the tension. And yes, Aunt Beckys are great - just put them into Google.

I'm puzzled by people who use the top of the thimble to push the needle through, though. Surely it's always meant to be the side of the thimble?

As for quilting to the edges, that's also not a problem using a rectangular frame. You're meant to leave 4" extra all the way around with the backing and batting, remember.

I wouldn't fancy a floor frame either. I can't do rocking stitch in all directions, I'm not fond of stab stitch, and it'd do my back in.

I have a 14" square hoop by Barnett Laptop Hoops. I have the sit upon to mount the hoop and the floor stand on order. You can just pull the hoop off and it has magnets to attach it to the other base. http://www.laptophoops.com/

I have to push in the needle from the top of the thimble. I can't seem to get it to go straight if I push from the side. I just turn my hand so the top of my finger faces the needle.

I also use the top of the thimble to push the needle through - I get a stronger, straighter stitch. I have a metal thimble with a rim around the top. I generally only use a thimble when I am hand quilting, not general hand sewing.