well the 2 platties could probably stay in the small tank if you want. taking the barb back is probably a good idea since you have mostly peaceful fish except for that guy. is the goldfish going into the bigger tank or is he going back to the store? be warned that goldfish are coldwater fish and don't do well in the water temperatures that other tropical fish require, so they shouldn't be mixed with tropicals.
plus goldfish get very large, and if kept in a small tank will be stunted which will lead to a shorter and more painful life as their organs will outgrow their skeletons over time (which is why most people won't recommend a goldfish for a small tank).
I would say that if none of your current fish get put in the new 10g tank, a dwarf gourami (make sure it's a dwarf as other gouramis will get way too big for a 10g tank) and a few platties OR danios would be fine.
those will require a pretty standard setup with filter, heater and thermometer which you can usually get as a kit from any petstore or (yuck!) wal-mart as well as a testing kit that will test for ammonia, nitrite and nitrate (get liquid tests, not strips as the strips are less reliable). If you buy the gear individually, I like my aquaclear HOB filter a lot, as you can do pretty much whatever you want with the media compartment as opposed to penguins and whispers which use "cartridges" and "bio-bags".
I also strongly suggest doign a fishless cycle on the new tank if you can be patient. in the long run it is much safer for fish (since there are none in there) and less work (aside from testing your parameters).