Shims are normally used to keep a toilet from rocking, but I suppose you could use them to try to level it as well. You'd want to use multiple points of contact (multiple shims) to do this so you weren't relying on a single point to prop the toilet to level. Depending on how high one side needs to go, you probably don't need a thicker wax ring, and no, the wax itself won't do anything. Whatever you do, you want to make sure that the toilet does not rock when finished, as that will break the wax seal and cause leaks. They make some composite shims that are easy to trim. the hard plastic ones are a pain, and the slope is kind of high, making it hard to get right and then to cut off. Caulk around the toilet base would hide them if you trim them well. You could probably shim the tank instead, but that might look weird.