it doesn't need a filter if you clean it everyday, but i would suggest it because it doesnt need it, but it helps YOU so u don't have to clean it that much. but you need turtle conditioner, it looks like a white block. without it, the chlorine and possibly chloramine(stays in water after leaving it overnight) can cause your turtle to have breathing problems and a soft shell.
basically a turtle needs,
-a place to bask (with natural light or artificial UV),
-clean tank ( I suggest using a filter)
-a tank is suitable for its size
and thats it
pretty easy, make sure you have the basics, anything not on this list is optional
like a heater(but if it is indoors your turtle should be okay, just make sure the water is not to cold). good luck, turtle are a bunch of fun