What's the worst they can do if u get catch fighting in public an will they send a warrant out for u if someone rats u out

To many variables to answer.

Depending on the circumstances, how badly someone is injured, if any weapons are involved,
the ages of the participants just to name a few.

Unless the police actually catch you, someone would have to go to the prosecutors office and fill out and sign an affidavit to charge you and have you arrested for this type of offense.

So, who looks better, you or the other guy?

Good question. I've been wondering about this.

My ex's new guy wants to "beat the crap out of me"

Let's just say... odds are 1 to 9 this kid lands a blow before he's on the ground.

My friends all tell me to confront this kid, but I don't want to. However, if this kid throws the first blow, I'm going to have to put this kid in a hospital.

... what're my options?

This is assault or assault and battery, ( or a dozen other names) each state in the US will have its own law on the issue, and each state will have what is required for the police to arrest you. If they arrive at the scene shortly after the fight and see people bleeding, they can often arrest on the statement of one or both of the people fighting, Depending on prior criminal history and the such it can be prison time, jail time or probation