I own a 172 and have driven a number of 172s and 182 cups and to be honest, I don't think there is that much in it. Others will have slight preferences either way but for me, a 172/182 are essentially similar, especially compared to say the differences between a 182 and the later 197/200s.
There are a number of threads on the differences so have a search and read people's opinions.
In your position, I would just try and find a really nice 172 and save a few extra dollars for the offset account. The only thing I wanted that a 182 had over a 172 was cruise control. This can be easily retro fitted.
172/182s need very little to be competent on the track. Other than normal stuff (fire extinguisher/ bonnet restraint) some fresh brake fluid and if you really want, some better front pads is all that is needed. A second set of rims so you don't trash your road tyres and your set.
Check out the for sale section for Beewrx21's 172. You will be hard pressed to find a better 172 and it already has a few upgrades that would make it perfect for a bit of track use.
Welcome and good luck in your search, hope to see you out at Phillip Island in an RS Clio!