I agree with BobbyBray up there. Because you have lucked on to this forum, you can now be quite cautious with any info from the LFS and double-check it with the members here. There are many knowledgeable and dedicated long-time fish enthusiasts who own fish stores, but they are the exception and even with them the advice may not be as good for you as what you can glean here, given some time and care. The knowledge and subsequent skills you build up will be your most valuable things for the hobby.
Be sure to think long and hard about whether there is any way to push your tank size even a little bigger. While a 10g is going to be ok if that's all you can do, every 5 gallons more that you can manage pushes you closer to the "sweet spot" of 25g, 30g or so that is much more ideal for a "beginner small tank." The not-so-obvious thing is that a larger volume of water is more forgiving of mistakes because it respresents a greater dilution of problems and a slower "change time" for things happening to the water. Makes sense if you think about it a bit. But the hobby is great and I don't mean to worry you if you can't make that happen.
The only thing I'll say about your first thoughts on what fish you want is that maybe the Barbs would be better as a thing to wait for after you graduate to a larger tank and to focus more on the schools of small tetras and danios and perhaps cories. Stocking is a good thing to be thinking about and working on all through your fishless cycling period.
Now, about that cycling! Be sure to search out the pinned articles (and the ones you'll find as links in the signature areas of experienced posters/members) that have to do with the Nitrogen Cycle and cycling. Its quite fascinating. What you want to do is saturate yourself with all the aspects of it you can find, regardless of whether you'll use it all. Its all a good core thing that helps you with the hobby from now on. The actual working document we usually use for beginners to get started is the one by rdd1952 and the Add & Wait method is the one used. The document works well as a starting guideline, but you'll want to start your own fishless cycling thread and post what you are doing, what's going on and what questions you have because there are any number of other aspects that come up that aren't necessarily in the guideline.
Good Luck and we'll see ya round! Oh, and welcome to TFF!
~~waterdrop~~