They both allow you to do the same thing, so there isn't much difference. It depends what you want to do with the qualification. If you wish to study in an English-speaking university, then in the UK, both are recognised and well-known. In the States, there might be a preference for the TOEFL as it is an American exam.
There are many ways to learn vocab and I'm not sure there is a best way. However, using the words you learn quickly is important. I'm learning Japanese and if I don't use a word much, I tend to forget it pretty quickly. I don't think lists of words help much as they tend to be a boring way of learning. I love browsing dictionaries and exploring for words.
Which grammar book is it? There's no point going over things you know, but start with what you know and see if the book just tells you the same or if it adds to your knowledge. If it doesn't, then move on to something new.
BTW- you wrote 'grammar' with one 'm' and used 'ways' with a singular verb. Welcome to the forum