First some basics:
for miniature painting we use acrylic colours and there are a lot of different brands available some are more famous among miniatures and scale models (because they have specific colours available, like the one you linked is a palette fur US WW2 military colours) some are more often used by artists and all of them have their advantages. The same with brushes and in the end it is more about personal preference and availability (makes no sense to buy the brand people say it is good but you have to order it while something of equal quality is available in the store around the corner and for a beginner a more basic set with ~10 basic colours is better than such a specific one)
For the brushes you want something similar to this https://www.amazon.com/Detailing-Watercolor-Miniature-Ergonomic-Precision/dp/B004HHIO50/ref=sr_1_10?keywords=army+painter+brushes&qid=1550092128&s=gateway&sr=8-10
in addition to the one you linked because you need more straight/fine detail ones and some larger one depending on the techniques used (dry brushing for example)
The only thing that I really recommend is to use a caned spray primer as colours won't stick very well to the pure plastic surface and you already have a basecoat if you use a coloured one. But it need to be a Primer and not a spray colour. I prefer Army Painter but mostly because of the colours available
Another thin would be Washes which are kind of thinner colours that add a translucent layer to the model or are used for blacklining
https://www.amazon.com/Army-Painter-Warpaints-Quickshade-Wash/dp/B0714QL55V/
(I also prefer Army Painter over Vallejo here, but the link is more for the example pictures)
For a beginner, a coloured Primer and a Wash can already give good (and fast) results on models like Stormtroopers
To clarify, I ordered the USA colors yesterday for my husband's birthday, is that considered a model color set? Also I see you recommended the Nuln Oil wash and the Agrax Earthshade, but the latter won't get here in time... do you think I'd be better off getting the Army Painter shade set in that case? I've seen it recommended by a lot of people. Or just the Nuln Oil? Thanks again for your help :)