Some of the advice given you by the person in the store was partly correct, but the majority was not, unfortunately.
First issue is the cycling one. In a new tank, ammonia and nitrite can reach toxic levels quickly, and a daily 50% water change (half the tank water) using a good water conditioner will probably save your fish. Prime is a good conditioner especially at the start, since it detoxifies ammonia, nitrite and nitrate. You can read more on the cycling issue here: http://www.tropicalfishkeeping.com/f...m-cycle-38617/
This link takes you to a "sticky" in the Freshwater section that explains cycling.
Now to the fish. The store person was correct that barbs need to be in groups; this is because they are what we call shoaling fish, though some people use the word schooling to mean the same thing. Such fish interact within the group, and in small numbers can be lonely, become aggressive, be very stressed--all this leads to poor health. Six is a good number for a group of most shoaling fish. But barbs are a bit different here.
Tiger Barbs should be in groups of 8 or preferably even more, and in at least a 30 gallon tank on their own. They have a tendency to nip fins of other fish if in small tanks or insufficient numbers. At this point, I will point you to our fish profiles section; second tab from the left in the blue bar across the top of the screen. We have many of the commonly-seen freshwater fish included, with information on tank sizes, numbers, compatibility, special needs, etc. You can also see the fish's profile by clicking on the shade name in posts (if it is exactly the same as the name in our profile it will automatically be shaded), for example, Tiger Barb (common name) or the scientific name too, Puntius anchisporus in this case. Please have a read of the profile information.
A 10g tank is not large enough for so many barbs, as you correctly guessed. And Tigers are not good fish for small tanks as I mentioned above. I would strongly suggest you return the Tiger Barbs. I would also return the Albino Barb. The Cherry barb will manage, but as you have 3 get 3 more. This will fill your 10 gallon tank. A small catfish for the bottom is possible, we can discuss that later.
Welcome to Tropical Fish Keeping forum; glad you found and joined us.