I enthusiastically recommend Chess Tempo (https://chesstempo.com/), which will give you interactive chess puzzles from real games that are tailored to your level. Someone else mentioned the similar system on lichess, which is also fine.
Because of that I doubt doing problems of the former kind will help seeing forks much when going back to “find the best move” type problems.
Before you can do that, you need to understand the moves you can make and their implications. I think identifying forks fit here.