There is no single correct way of writing. The principal aim is communication. That is why getting the grammar and spelling right is important; mistakes get in the way of communication. The same goes for idiom.
It has to be said that much academic writing is often not very good: jargon is rife, and much is written that is unnecessarily complicated. As a general rule, be simple, be direct. Think what you want to say, and say it as straightforwardly as you can.
Perhaps most importantly, work with each other. You will all be bringing different skills with you. Share them. Pass round your essays once they have been marked (particularly if they are good). It’s not about competition, but helping each other. Talk to people in the years above you – they’ve been here longer, and can give you some very useful pointers.