AAAaaakkkk! I can't believe I'm answering a post about Wal-Mart Schwinns.... but hey, it's Christmas!
Changing the front sprocket is probably a good idea. I saw one of these bikes yesterday that had a front sprocket bent like a Pringles Potatoe chip. The owner told me that his older brother (a quite large kid) had bent it whilst trying to accellerate rapidly. Exactly how this happened, I do not know... but I did see the bike, and the sprocket is twisted to all heck.
It was rather easy to swap out the ruined sprocket with an old 44t out of my parts box. (I THINK the one I put on it came from a '60's vintage Sears Stingray-clone, but I'm not sure. ) I DID notice that the 44T had very little clearance with the frame, so it is unlikely that anything larger would fit.
I also had to lengthen the chain by a few links.... and discovered that the chain that came on the bike is a little different than a standard chain, so the extra links I had in my box would not work. I wound up tossing the chain and putting on a different one from a junker bike.
As far as teeth go..... stick with a 44T unless the bike is going to be ridden by a very little kid. With the 36T, the rider will pedal and pedal and go virtually nowhere.