Am I shooting myself in the foot by going to a mid-tier university for a PhD? Should I try to transfer after my masters?

I am currently in a graduate program ranked in the mid 50's in comp sci according to us news. I will start my program in the fall. I am really leaning towards getting a PhD because I like research and the relative freedom that comes with the degree, however, I am not sure if it would be wiser to try to stay here for my phd or leave after I get my masters (it would be very easy to do because I am currently funded only by a 2 year teaching assistantship). Would it be relatively easy to get funding to go to a higher ranked uni with a masters assuming I get good grades and perhaps a publication? Another factor: I am going to the same uni as my undergrad, is inbreeding a factor?

Thanks!