What should I look for in purchasing a replacement recessed light?
Unfortunately, many LED retrofit kits do not fit the standard incandescent housing. You may find yourself trying many before finding one that works. Each manufacturer may have slight differences. In addition,  if you find one to fit, you may have other issues, such as dimming mismatched technology or tripping breakers. If you are only looking to reuse the actual cans, and change out all other componants, you may utilize your time and money more productively by purchasing complete kits and replacing the entire can.  You may not actually have to even adapt the side of the hole, as the attachments used in many manufactures kits allow for some devience. A major plus, you have a complete lighting system that 
comes with everything included. Good luck!