Having kept and seen many turtles in aquariums.
#1 I advise against it, almost always the turtles become stunted or deformed even in the best of care when an aquarium is involved.
But if you insist I would say a slider needs a 6 ft. x2 ft. tank minimum for healthy development along with proper lighting, diet, and supplements. I always found tank size was more important than pristine water quality, but I would still advise put on as much filtration as possible. Turtles will survive in aquariums that can cause major issues later on in life and I would argue only ones that have done well and developed a natural adult appearance without ridiculous care where musk turtles and snapping turtles. Red ears often develop a dome shaped shell in the aquarium, resembling a tortoise and nothing like the more streamlined shell of their river brethren. Also watch that he doesn't cut his neck on the shell swimming into the glass.
Many people keep these turtles in tanks 30-55 gallon in size their whole life and don't have the exposure to wild caught specimens to know what they are supposed to look like. Yeah your animal could probably live for live in a 55 gallon tank but the animals physical development suffers.
My best experience(and recommendation) with turtle keeping was outside in a pond with a netting or wire cover to keep out racoons and then you hibernate them in the winter in a container in your fridge.