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Should I use .032" or .062" copper clad to make my own PCBs?

In all of the tutorials for making your own PCBs, I've never seen the thickness of the copper discussed. Does one work better than the other for home etchings? I plan to use muriatic acid.

Side note: does RadioShack still carry copper clad in stores? It's not on the website anymore, and I don't go to RS on a regular basis to check.