Buying something with better than 2meter accuracy is probably more money than you want to spend. You can get to roughly a meter accuracy for somewhere around $750-1000 if I remember correctly. That's probably changed by now. Basically cost goes up exponentially with accuracy.
It's a good research project though, to learn about the different types of receivers and the different types of correction to make them more accurate.
If you're willing to stay about 10 feet from the property lines, there's a lot of units that can get you there for a few hundred bucks (or use a cell phone).
Like I said, research project.