What is a starter cell?
Nice question - this terminology isn't referring to a special type of cell or anything, but to a peculiarity of the technique they are using.

They are labeling a subset of cells with rabies virus; rabies then travels in retrograde fashion to presynaptic cells, and labels those as well.

The "starter cells" are those initially infected cells, where the tracing "starts." This reference more explicitly states this terminology, and talks about the technique extensively, I would strongly recommend it for helping to understand the paper you are reading.