Any patches will do. Feather edge are better but not vital. There's a lot of BS spoken these days about puncture repairs but the reality is that as long as the glue & patch are properly applied - it's as easy to it properly as it is do it wrong - the repair will be at least as strong as the original tube & probably better.
A trip to your LBS should see you stocked up with what you need.
My evidence for this is that as a 'cyclist' I go through stages where the default gift is a cheap set of lights or similar, and occasionally the cheapest nastiest repair kits known to man, but they all work as long as the patch is applied properly. Patches coming adrift is an unknown here.
There was a hole in the new tube, too. Hmmm, there must be a lesson to be learnt here.
Rapha carbon fibre patches, for better power transfer and decreased aerodynamic drag. £120 for five patches, but they're worth it. They'll knock minutes off your personal best. Don't believe the sceptics.
I wish I'd read this on Saturday. A hour and half into Sunday's ride I hit a pothole and punctured both front and rear! The spare tube sorted one. The solid cement in the repair kit didn't sort the other ..... A passing local rescued me - he put me and bike in his car and ferried back to my own car. Incidentally, when I got home I took a new tube out of its box and replaced the punctured one. 2 minutes later I return to the bike and ... yes the tyre was flat! There was a hole in the new tube, too. Hmmm, there must be a lesson to be learnt here.