Tires

So one front tire is showing cords, it's time for new tires. I don't know if you guys know much but I figure it's worth a shot. My current tires are 245 Michelin Pilot Sport A/S Plus. They are currently 224 per tire. My parents would prefer me to stay with all seasons, but in Texas I'm not sure that matters. After some research I think my best bet is Continental extreme contact DW (Summer tires, 127 per). Good handling and great in the rain. The problem? I might only be able to afford two of them at the moment. Can I run summer tires in the rear of my Mustang and all season up front for a little while or will that not work? Any other recommendations? Now I'm debating if I should take my car to the body shop to get an estimate after getting rear ended over a month ago. Tuesday might be my only chance to go. I'm not sure driving on cords is a great idea, it's on the outside of the tire. The timing couldn't be better for this to happen. Thanks for any suggestions.