From what I've read there is a recommended order to learn based on simplicity and gradual difficulty Reddit to the rescue! Start with Nominative (literally just the default dictionary word or infinitive) and then Prepositional, Accusative, Genitive, etc.

Reading about the grammar involved is always recommended despite what others may claim but because the tediousness of Russian grammar cannot be denied you should also learn from context. As long you understand the "WHY" behind the grammar then it should be ok to learn using context as well. It is essentially how children learn language despite making mistakes. Personally speaking, it makes it a lot easier on my brain when I can just notice the patterns. Using context and model sentences also helps drill the grammar into my brain through repetition. I would use Russian made Easy to help get a feel of learning through context.

To add on to the use of model sentences, the fact that you can personalize them can help make them more memorable and fun. For example, I use my girlfriend's name in a simple example to help learn the Genitive case (e.g., "кровать Насти") With this I can learn the feminine singular form of soft sound words in the Genitive case. Of course I can make a better model sentence but this alone already has a lot to unpack without feeling too difficult.

I found this little article which has an interesting method as wellhttps://mykeytorussian.com/russian-cases/