OK,
What do you think about Gobies and Firefish? - Love em
Purple firefish, - Yep
Exquisite firefish? - Yep
Neon blue goby? - Yep
Orange stripe prawn goby? - Yep
Cave transparent goby? - Yep, but never heard of it
And maybe possum wrasse? - Yep
Can I mix them? - Yep
One of each? No. Too many fishes, and likely aggression between similar fishes
So a few things worth mentioning:
Aggression can be caused by or exacerbated by:
Not enough places for fishes to hide (tank size or rock/cave density)
Fishes being in the same food sphere (i.e. too many planktivores competing for food midway in the water column)
Fishes just not getting along with non-mated similar or same species inhabitants (i.e. firefishes that are same or different colored but not paired probably won't get along, and will either kill each other directly, or chase each other out of the tank until one jumps and dies)
I generally try to use those rules when making my decisions. The firefish, I'd recommend either getting a pair or trio from the get-go (i.e. mated pair/trio), gobies, maybe one or two will be fine in a 20g Long tank, so there is plenty of wide area. Neon goby and wrasse should be fine, because other than in name, the goby doesn't look like or feed like the other two gobies (or other inhabitants), and the wrasse will largely be independent.
It is also very worthwhile to check out
this compatibility chart that LiveAquaria offers on their website.
And it's also worth mentioning that in this hobby, for better or worse, there are very few black and white rules. Have people filled a small tank with a ton of fishes of the same variety and kept it that way for a long time? Probably. Were they successful? Probably not, but maybe it depends on your definition of success. Maybe they had to constantly feed tons of food to keep aggression low, but as a result, their tank was covered with algae and the fishes weren't healthy because of the always-high ammonia-nitrite-nitrate levels even with heavy skimming and frequent water changes.
It's all about what you want your tank to be, and how you feel comfortable keeping fishes. When I bought my first 24g nanocube used, it came with 13 fishes, including a yellow tang. I immediately traded all of the fishes in except 3-4 small fishes. My big 120g tank I had probably 12-15 fishes, including a few large tangs, and everything did really well. Its all about what you want to do with the tank, and again I think it's important to keep in mind that the traditional view of "oh, I'm only keeping fishes so water quality doesn't matter" isn't true unless you also like keeping lots of algae and unhealthy fishes.