First I got slow sinking food, because it was the most floaty food I could get. I think I overfed them though for the first three days...
Now I have tropical semi-floating pellets. They should be better, but there's still food on the bottom. Not good.
How much did you feed? Since you didn't cycle your tank, ammonia toxicity will be a problem. I'll get on this in a second, but for now, only feed what they'll eat in about a minute every 2-3 days. They'll be able to live on this much food indefinitely. They'll be hungry, but they won't poop as much, as I'll get to.
The barbs don't eat very much, at least not when I'm watching.
To add to this, The water has gotten partially blurry. You can see it if you look a tad closely, that the water isn't all crystal clear.
Culturing the tank is a big "if" too.
As you decribe, the tank isn't cycled (pet store advice to leave it running does nothing at all to cycle the tank, an ammonia source is necessary. In your case, fish poop), and this is almost certainly to blame for both problems. Please review this thread:
<a href="http/www.fishforums.net/index.php?showtopic=175355" target="_blank">http/www.fishforums.net/index.php?showtopic=175355</a>
You'll need a liquid test kit ASAP. In the mean time, do a 50% water change and gravel vacuum regardless, the tank most certainly needs it.
The blurriness is likely a bacterial bloom. There's a lot of confusion and misinformation on this. The bloom itself is harmless, but is usually tied to conditions that aren't helpful. It's not the good bacteria catching up, as many stores and even some books say, it's the bacteria that break down fish poop catching up - it will actually cause an increase in the rate ammonia is released, which is bad for your fish.
If you've received the very common advice that water changes slow down a cycle, forget it. Dr. Hovanec actually found the ideal bacteria growth happens around 0.14ppm, which is half of what the above thread suggests as a maximum for ammonia and nitrite. Even the undetectable ammonia reading in a fully cycled tank is enough - an uncycled filter running alongside a mature one will become cycled over the course of a few weeks.
Lastly, I bought some bacteria in a bottle, and I don't know if this stuff actually works.
They range from snake oil (many brands contain the wrong bacteria or no bacteria at all) to unreliable. The most successful brands are refrigerated products, Bio-Spira (US, however due to the owner of the patent leaving the manufacturer, this product was recently repackaged and is no longer the refrigerated baggies it used to be) and Bactinettes (UK), but are still susceptible to all manner of mishandling. A small handful of brands are actually made quite effectively - the water in the bottle will be brown and smell bad. In this case, many are just dead bacteria, it's usually best to massively overdose (dump the whole bottle in) and hope for the best. Since you bought it, you might as well use it, but don't expect miracles, the overwhelming majority of experience on this forum has been that these products fail to live up to the claims on the bottle (if not fail entirely).
I don't even know what to do with stocking...
I'm planning on two platys, two swordtails, five gold barbs, and five tetras.
I wonder though if it's too much.
For now, don't add anything until the cycle is completed, and slowly afterwards to avoid a "mini-cycle" as your fish load exceeds the filter's bacteria capacity. Mini-cycles are handled just like a full cycle, but where a full cycle can last a month, a mini-cycle typically lasts a couple days to a week at most.
Once the tank is cycled, a good range to shoot for is 1" of adult size per US gallon as a starting point. This rule only applies to fish under 4-6 inches, and there's lots of reasons why it's not accurate, but it is an underestimate.
A tank that's been running for about 6 months can sustain 1.5" per gallon, sometimes up to 2" per gallon or slightly over - this takes a flawless maintenance routine and strong filtration, however. In a mature tank, there's more art than science in stocking, so monitoring water quality continuously through the tank's life is important.
To look at your stocking list:
2 platys: 4"
2 swordtails: 6"
5 gold barbs: 10"
5 tetras: 5-15", depending on species - I'm going to assume mid road like black skirt or serpae and say 10.
This brings you to about 30". This is a good stocking to aim at while the tank is still new. When it's mature, you should have some more room to play with - I'd suggest a group of 5-6 corydora catfish, and a centerpiece like a pair of dwarf cichlids or a pearl gourami, maybe even an angelfish. For gouramis or angelfish, research the tetra you decide on, as many are actually somewhat aggressive and will nip at slow moving fish with long fins. Angelfish are also likely to eat neon tetras. There's some tricks to being successful with the two, but the neons won't live as long as the angel, and afterwards you won't be able to introduce a new neon shoal.
With the platys and swordtails, I'd suggest getting all males, or two female platys and one female swordtail. It's a good idea with livebearers to have 2-3 females per male, as the males are very hyper about mating, and will hound females constantly. Having several females gives them some reprieve as he spreads his attentions around. Since platys and swordtails are closely related, they will readily cross breed, and you can count females of both species in the gender ratio.