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The radio is a separate entity to the ROM. Usually you can just stick with the radio you have and you won't have any problems.
Some custom ROM devs recommend a radio, but I assume that's only because they can only guarantee it works with the one they use.
Once you get into the swing of things, you can have ROM Manager download a new rom and have it backup, factory reset and install the ROM + google apps in one go.
I do think it's a good idea to go with just the backup on it's own first like you are though, just in case.
In this case, you definitely need to do both types of wipe.