Hi RusselB. Yes, checkboxes would be your best option for what you're looking to do. And, if it's necessary to make one of the checkboxes not available when another is checked, that is easy to do as well with either an automatic uncheck/check command when you click the other one, or by enabling/disabling it when you click the other one.
As for the groups, I think that if you use groups, everything has to be grouped (so you'd need 2 groups).
