First of all, 1/4" of gravel is not going to be of much help when growing plants.
I use about 1.5" in the front, sloping up to 4 - 4.5" in the back for taller plants. My depth is more than most people use, I think.
I don't know why anyone would tell you to cut down to 1/4".
Can you give us a rough estimate of the size of the gravel in mms.? You might want to add back to your substrate with a more plant friendly material, since you've got much of it out anyway.
Your heat does not have to be that high for a planted tank. 76° or so would do fine.
An AC MINI is kind of small for a 20 gal. tank, but if you keep your fish load down it should be OK, if cleaned regularly.
There is another member starting out with plants, just as you are, named Blinky I think. Read his/her post and responses to it for more info. I left a link on my reply, for a really nice site that would probably help you and answer some of your questions as well.
Len