The best set up regardless of how small or big for aquatic turtles I found to be similar to how you would set up a river tank. I had a 60 gallon that was up for 7 years before the tank was accidently broken. The only turtles I had in there were hatchlings, but this set up is ideal for any sized environment to house an aquatic turtle.
The tank should be half filled with water. Make land areas rising from the water strategically placing rocks, wood and slate rock from one side of the tank to the other, leaving a large open swimming area underneathe and preferrably up front. A bridge basically. I lined the wood and rocks with peat moss...nice and thick for padding. I let edges of wood and slate rock serve as ladders for easy mobility onto land. The water must be deep enough for the turtle to be completely submerged and able to freely swim about. If a turtle is incapable of such in a tank half filled with water, then the enclosure is too small.
My filtering was simple, but I had small animals and mostly minnows, fire belly toads, fire belly newts and rubber eels. On occassion I took in other fish such as catfish and angels, but they were rescues and temporary.
I had a powerhead's intake embedded in a larger sponge. The out take was lead by a hose that ran to the top of a land cave in the middle of the tank. The filter bag filled with carbon and zeolite was tied to the end of the hose that rested on top of the cave and covered in peat moss to hide it. The rocks and wood the cave was made of served as bio media as well as the peat moss. Peat moss is great, but there is a downfall if you are keeping fish that require high pH values. Peat moss is media that will bring the pH down. It's a natural buffer. The waterfall is an awesome effect.
I thoroughly rinsed the sponge in tap water every week. I didn't worry about losing bio, because the wood, rocks and peat moss held enough. The sponge was the mechanical part of filtering. Peat moss was rinsed on occassion in used tank water. I just scooped out some water from the tank and cleaned it in a bucket. Once every six months or so I would rinse the peat under tap, but a section at a time rather than all of it at once. I also had a second water pump to circulate the water...out take pointed to the middle back glass panel, so the water would bounce off the side and go into a circular motion around the tank. This maximizes effectiveness from your equipment.
For a three incher...the same can apply, just make everything bigger or more...like more sponge to catch solid waste...more bio media to accomidate the large waste load of a larger turtle and stronger water pumps, etc. Instead of a sponge embedded powerhead, you can use external filters, just run the hoses properly for the type of filter. This sort of setting allows you to be creative with effective filtering without it breaking your wallet. Use the environment you set up to help you maintain the waste load.