I wouldn't. A biofilter runs high nitrate, which is incompatible with a reef, and not good for fish. It takes live rock and sandbed to break the nitrate down to nitrogen, which is where it needs to go. It is so serious for a reef that I don't even keep sponges in the system, because they can also spike nitrate.
A skimmer removes spare amino acids from a system, so it is not a filter in the ordinary sense. It is definitely useful for a marine tank, but a very small system might get by without; and reefs other than sps don't need a top-of-the-line skimmer because corals are also filters, and will enjoy a certain amount of extra nutrient, but not too much.
Some people also run filter socks, which are simply a dense cloth bag that has to be removed and cleaned often, to get the least particulate out.
Bioballs are useful in a fish-only, but frankly, I find a fish-only not as easy as a middling sort of reef, which lets you know (by folding up) whether your water is needing a test and correction. Fish just tough it out until they go belly up: so if you keep fish only, you do need a strict testing schedule.