IMO - I would see if you can clear off the CO with Verizon (depending on what the charge is and if you can fight it).
As far as the medical bills - AFAIK - it's possible to reach out to billing and see if they can recall the bill - another thing you can try is called charity case (or something along those lines where they either reduce the debt or cancel it completely) however, YEMV.
As far as your scores go, IMHO - you might get approved but may have a low limit. I would suggest clearing the baddies up first before applying.
Good luck!