To answer this question, let’s all think about it a little bit.
Do I need to know the difference between American English and British English?
You need to know that there are differences. There are few different spelling rules, grammar rules and, of course, different accents and vocabulary. You need to know that there are those differences but that doesn't necessarily mean that you need to study and learn them.
The truth is that all English speakers understand each other, despite their differences. They watch each other's movies, read each other's books and news, work with each other and so on. They are all capable to understand each other.
Should I care about the differences between American English and British English?
Maybe. It depends on why you're learning English. You only need to care about the differences if you're studying for an English exam, you're applying for or attending an English university or you're using English professionally for your job.
Usually, you need to pay attention to the spelling and grammar rules because they can affect your score or even affect your reputation. So if this sounds like you, then you definitely do need to think about whether British English or American English is the right choice for you.
So which one is right? Which one should I use?
You need to think about yourself and your situation. Are you living in an English-speaking country? Then, of course, use the type of English that is used there.
But maybe you're planning to study in an English-speaking country. Which one? If it's America, then you should be training to learn American English. But if not, then focus on British English because most other English-speaking countries use British English grammar and spelling standards.
Do you speak to a lot of clients or colleagues who are from America or the UK? This can help you to decide whether you need to study American English or British English. You might think that one type of English is easier than the other and that can also tell you which one you should study. You could choose any of these reasons to help you decide which type of English to study.
So focus on either British or American English but remember that the other one exists. You don't have to choose one over the other.