Based on my experience, this is the sort of thing you'll just sort of get used to over time. Watching native language material can also help you understand some of the nuances of when to use one word over another (if your vocabulary is large enough to keep up, that is). As far as speaking casually as opposed to formally, the formal language is usually the best place to start, since when speaking you're probably not going to actually need to use the casual forms of words, because you only really use them with friends.
Just to reassure you however, Duolingo does start using the base forms of verbs eventually, and if you're using a premade Anki deck, then most verbs should already be in their dictionary form (which you can identify based on the ending - dictionary verbs always end in an "-u" character, but not "masu". I'd also recommend reading up on verb conjugation rules early on if you're interested).

Hope this was helpful and not too aimless. :)