Turtles are messy. Most turtle do get big. You have to check with state laws to see what turtles are legal to keep. I would recommend a 40 gallon breeder tank. One more thing- water turtles can live to be 80 years old. If you get a baby plan on putting them in your will. My mom has a red-eared and i'm getting her when i'm an adult (i'm only 13). You can use a filter, but prepare to spend good money on it. You need a pretty good filter to keep a turtle tank clean and even then you'll have to change it a lot.
Turtles can stink, and it's recommended to put a GOOD filter in the tank. Some people will say red-eared sliders, but they can actually get 18" long...way too big for most tanks. The African side-necked turtle can get 8" long. Painted turtles can get approximately 7-10" long. As for others, I'm not too sure as to what size most of them get. For any turtle, though, I would recommend getting a 40 gallon breeder tank.
But you can eliminate the really bad smells by investing in a lot of good quality filtration.
I would use a good Powerhead water pump and making a custom filtration system. I see some people using those Hang on filters, but you would need to at least have the water level half way, depending on the height of the tank you have.
Yes, you can put a filter, but your question is quite vauge.
1. What kind of turtle?
2. What size of tank?
3. What kind of filter? Hang on? Canister? Sump? Custom?