I have a couple of wet/dry filters. I do them on the cheap. I use a 29 to 55 gallon sump. You can use a big rubbermaid container to really keep costs down. The pump is dependent on how big the whole thing is and how much water you want to move. My tanks are drilled for the overflows. There are ways to avoid it but I have found that overflows can get clogged so I always do two now.
For the filter you can use a number of things. My favorite is an empty cat litter container. I wouldn't have a cat but I watch for them in my neighbors recycle. These are somewhat square containers which makes them easier to suspend them over my sump. A round bucket would work but the round thing isn't as easy to support. I just punch lots of holes in the bottom of the bucket. I have used two by fours, acrylic, and a plastic shelf sitting in the sump. All of these worked pretty well.
For filter material you can use your imagination. Bio-balls and the like can get expensive. Sometimes you can find women's platic curlers in the dollar store. These worked great for me years ago. Now I use some bio-balls I got cheap at an auction and filter material from Aquatic Eco Systems. There are all sorts of things that work.
As you can tell this isn't something I like to spend money on. If you wanted more detail on how I did any of this, let me know.
George