What sort of biofiltration is best for a small, portable, biofiltration unit?
Any kind of sponge and pump filters will breed nitro bacteria to remove organic content. Added to a drip filter made from pure mineral sands and clays, you'd have a bacterial sponge and plant aquarium plus a sand filter.

You can make you own activated carbon too.

Urine requires at heavy plant growth to purify. You already have a tank, volume not given so I'll say it's 125 L. Here's a two stage bio filter: one with an incoming and circular bacterial filter to filter incoming water in graded sponges up to about .05 - 1 mm finest incoming particles for foods and stuff.  Use 2 divisions in the tank, one of 100 L, one of 25 L that you can prepare 10 L from every day. 

Use 2 fish filters AC of 7 - 20 watts (?) or 12 V (DC) pumps similar to fish ones. Use 500 ml - 1L volume of filter sponges with fast access so you can squeeze out the bacterisl mats periodically because they will fill with nitrogen and phosphate and oxygen based pond organisms.

If you can fill the 100 liter tank with algea, it's ideal.

Put a valve to keep 2nd 25 L tank separate. Filter final 10 L drawn daily through mountain mineral sand from places with great spring water, i.e. dolomites / chalky to add trace elements. It's recommended you use sunlight and lots of plants in the first tank.