IMHO, internal wiring does not do all the much, that being said, I have never used any exotic wire, just OFC copper. Unless I'm putting in a new XO, usually just keep the OEM wire.
Also from experience, take a picture of all the connectors before you remove any of them. If any of the terminals are not marked +/- mark them before removing anything!!!!! Nothing is worse than spending hours swapping parts out, only to have something out of phase. It will never sound good, and you will curse yourself chasing it down. Woofers are usually easy, mids/highs can be tough to tell phase.
Crossovers will yield huge benefits! However, it will also cost a lot to do correctly. Spending $20 on a single resistor, or over $100 on one cap. Just know, for a 3 way, simple XO it can be $500 in parts.
Don't forget the binding post, this is another area where most manufactures cut corners. Even speakers that cost $10k can have $10 binding post in them. Take a magnet to them, if it sticks, you want new post.