Melanie, the smaller ones would work fine, depending upon the size you wish to seal. I make a lot of children's tray puzzles, typically A4 size so the smallest I could use for this would be the 12" so I just got the larger one, which has come in handy when I have made larger puzzles. I don't use bags, I purchased a roll of the heat seal plastic years ago and have wrapped hundreds of puzzles and it wouldn't be 1/4 gone. The plastic on the roll is folded in half so a 300mm (12") roll would allow you to package something almost 300mm wide by as long as the sealer, you can seal longer by flipping the package over and sealing from the other side eg almost 600mm.
You are correct they just seal the plastic and a heat gun shrinks the wrap tightly and with a bit of practice you can get it almost without wrinkles.