I wouldn't recommend starting with grammar. Grammar is best learned in context.
If you're going to rote-learn cases, the best way to do it is by memorising sentences. So for accusative you could memorise the following sentences:
To je čovek. Vidim čoveka
. (masculine animate)
That is a person. I see the person.
To je kompjuter. Uključujem kompjuter.
That is a computer. I turn the computer on (masculine non-animate)
To je jabuka. Jedem jabuku
That is an apple. I eat the apple.
To je dijete. Vidim dijete.
That is a child. I see the child.
Then try and look for other example sentences. The more you see and use the cases the more automatic they'll become. It's good to get some of the theory down but lots of theory without actual exposure to the language is useless, so make sure you're supplementing any explicit grammar study with learning vocabulary, or general exposure to media (such as music, TV, or internet forums - the "Serbia" and "Croatia" subreddits are quite active and would be easy reading for once you get to an intermediate level, just remember to look at slang dictionaries like Vukajlija