Don’t plan on a CLT base for Republic.

Live in base whenever you can.

RDU commute to RAH base would be doable but it would be commuting and, see comment 2.

I had an offer at PSA as well but chose Republic. I’m happy with the decision but I would have been commuting either way. If your only options are RDU And CLT then I would focus on airlines that have bases there first. It makes a huge difference.