Of course, you should learn both at the same time! But if you have some vocabulary and bad grammar, people will still (probably) understand you. If you have great grammar but no words, you won't be able to speak. Think of words like they are boxes in a warehouse: it's great to have a plan to organize them (in other words, grammar) but if you only have the plan and have no boxes, it won't do you any good.

In your case, you're already able to express yourself and the grammar in your question and on your profile is good, so it's not really a question of what to do "first." I'd say you're on the right track already. Language is for communication, so one starts by learning the most common vocabulary first, and the most common structures for forming sentences. These structures are often referred to as "grammar," but that word tends to have negative associations for most people, due to bad experiences at school.

You need a chicken to make an egg. And you need an egg to make a chicken. Grammar and vocabulary are just the same. "Brrr.. cluck cluck.. cluck!"

Don't study grammar on its own - it's boring and pointless. Likewise, don't try to memorise lists of words on their own either - that's pretty boring and pointless, too. Start with basic useful phrases, and then move on to more complex ones, expanding your vocabulary and developing your understanding of grammar as you progress.