As dwarfgourami has said, it's the mix of fish that matter, not whether they're related. In fact a "family" means something very specific in biology, and within a family diversity can be considerable. Pike livebearers and guppies both belong to the same family (Poecilidae) but couldn't be more different as far as aquarium care goes!
As a broad rule, I find the following ideas work well:
1) Fish of the same size mix best visually. If all the fish are of totally different sizes, even if they get along behaviourally, the "visual" can be cluttered and busy, especially in smaller aquaria. So for example kissing gouramis and guppies would probably coexist, but they wouldn't look that good. Kissing gouramis and larger rainbowfish or barbs, on the other hand, complement one another.
2) I go with the ratio 1:2:1 when mixing fish. This is one surface dweller for every two midwater fish and every one bottom dweller. So you could go with one danio to two neons to one Corydoras, for example. Not that I mean just keep one danio, but rather for every one danio, get two neons.
3) Lots of a few species look better than a few specimens of lots of species. So, instead of three zebra danios and three pearl danios, get six of just one species. The result is that the fish school properly. Even where fish don't school, as with, say, gouramis, you can get to watch the animals interact. Of course, this is only safe where the tank is big enough for (typically) aggressive males to get away from one another if need be. So read up on any species before buying more than one specimen.
In a 10-15 gallon tank, your best bet is either to keep a pair of something entertaining and breedable (say, a pair of dwarf cichlids) or else go with a school of some "mini fish" that would be complemented by a nice arrangement of easy plants such as Java ferns. Small danios, dwarf barbs, dwarf Corydoras, and so on would fit the bill nicely. Trying to do too much in a small tank is tricky and you can easily end up with a jumble of fish. Personally, I like keeping pairs of fish in small tanks and trying my hand at breeding. This is very engaging, and with livebearers in particular not inordinately difficult. There are some "rare" livebearers in the hobby that are both pretty and fairly easy to breed, but yet uncommonly bred, and so become a very nice achievement as and when you get a brood. Selling rare livebearer fry isn't difficult, either.
Cheers,
Neale