The word "meet" has two basic meanings:

1. To see and speak with someone for the first time.
2. To get together with someone who you already know or have met before.

The phrase "meet up" is useful because it only means the second definition of "meet". So it's better to say that you're "meeting up" with someone who you already know:

Let's meet up next weekend.

If you say that you're "meeting" someone, it may sound like you don't know them yet.

To identify the person that you're meeting, use "meet up with ___":

I met up with Jerry for drinks the other day, and he told me that you were engaged. Congratulations!