There are some ways that brain teasers can be classified, categories can include, Logic Puzzles, Word Puzzles, Visual Puzzles, Lateral Thinking, Deduction. I think it really depends on the site or book you are using. I own one Mensa book of puzzles that only categorizes by level of difficulty but another that actually puts all kinds of word puzzles in a different section. So the trick is to just find a book or site that you like their sorting methodology.
I also find that there are different that everyone is good at at least one kind of brain teasers, so just keep searching until you find a kind you enjoy and then branch out from there
Gluck and remember, you will get better with time