The only must have tool: a sewing machine with a FMQ foot. There are many different kinds of feet you can use, but all of them will work. You just have to find your preference I did find a better sewing machine = better quilting. Sad but true. A very very skilled quilter could probably do well on a cheap machine, but when I upgraded my Kenmore 16221 to a Bernina 430, I was suddenly a better quilter.
The tools I prefer:
-A closed toe (metal) foot if I am doing large scale quilting (because my threads get caught on the open toe foot...) an open toe foot (metal) if I am doing small scale quilting (because I need the visibility). I've had a plastic foot before, but didn't love it, others do. My feet do not hop. I like that.
-Machingers gloves if the quilt is larger than a lap size. Smaller I don't use them because they make my hands sweat, but I need them for traction on larger quilts.
-Gidget table to recess my machine.
-Folding table for "outfeed" behind the machine and ironing board on the left side of me, to help support the quilt's weight.
Another tool I have, but haven't really noticed a difference when I forget to use it
-Supreme Slider (I've even FMQed without it, with the feed dogs up, with a normal stitch length, and everything still turned out okay.)
I do usually put my feed dogs down.
I really love Connecting Threads Essential thread for meandering quilting, as it is thick enough to show. When I do designs that trace over themselves, I use Isacord embroidery thread. It is strong enough to not break, and thin enough to not get ugly when there are many layers of it.
And yes, Leah Day is a genius.