Sounds as if you are off to a good start. You have enough drawn comb for the packages to get a good beginning. Hopefully the combs have some feed.
If you are drawing new combs, your bees should do fine in the boxes you have in mind.
Personally, I used to sell wood frames with plastic foundation at the market and people scooped the honey off, then returned them to get have them reused.
You can also go with wax foundation or empty frames, but the bees may build across in the latter case unless there are drawn frames on either side.
As for the cell size, frankly, I would not worry about it except for brood comb, and even then, not so much.
> I was thinking about getting those supra kits and putting them on top of the deeps.
I'm not familiar with them, but have made plenty of Ross Rounds.