We are creating a lead nurture program where if a new lead is created AND fills out a form, they will be added to the nurture program. I know that if you have 2 triggers in the smart list, that if a lead qualifies for either of them that they will go through the campaign. Advanced logic does not work on those. We don't want preexisting leads to enter the program. What is the best way we can achieve this?
That's subject to a race condition.
The way to do it is a [Form Name is not empty] constraint on the Person is Created trigger. You need to interlock activities as much as you can, and constraints guarantee you're looking at a single atomic activity.
Assuming that's what the OP meant — that the form created the lead.