My partner and I are having our engagement party at the end of this month and I just wanted to see if we needed to talk about each other in the speeches or more or less just thank everyone.

A basic speech goes something like this
Prepare your speech well in advance. Having everything thought out in advance will make your speech more fluid. It will also help you organize your thoughts, make sure you've left nothing out and help you eliminate inappropriate or questionable jokes and comments.
Step2
Start by thanking the guests for coming to the engagement party. You should also welcome and acknowledge family members from both sides.
Step3
Thank everyone who helped out with the engagement party, including family, friends, caterers and servers. This should only take a minute or two, but will go a long way in making people feel appreciated and respected.
Step4
Switch perspective by bringing up a touching or funny anecdote about the couple. When you know the bride better than the groom, it's fine to make the focus of the story on her, or vice versa. The important thing is to make the speech both personal and entertaining.

I would mainly thank everybody and say how you are looking forward to spending many good years with your partner.