Really confused about what tire size to get

so i was recently trying to get my summers on and they said the tires were no good. no problem. i got my car and tried looking online for the tire size, but i immediately was confused because after looking at different sites the tire sizes for my car were all different. On my car door, it says 225/45 R 17 front and back. The tires the previous owner had on it for the summer were 225/40 R 18 and 255/35 RF 18. i need sport tires for a sport car and when i tried looking on continental they list the 225/40 R 18 for the front and the 255/35 R 18 for the rear. should i stick with what was on the car or should i get what is on the door?