How much harder is it these days to get into a PhD program without having a high ranking degree for UG? [D]

I'm going to my state school (R1 public university) and hope to pursue a PhD. How hard is it to be accepted to high ranked PhD programs in this field without going to a t5 university like Stanford or MIT? The network connections is obviously going to be stronger at these schools so would it be more worthwhile trying to get a better Masters degree that is more name-brand before applying for PhDs?