If we are imagining a scenario where time travel is possible, then I cannot see a reason why you should be unable to travel back to an event that took place before your birth (unless that is a specific restriction of the time travel mechanic such as Quantum Leap rules).
Your personal timeline would be consistent, eg:
1990 -age 0- born
2015 - age 25 - discover time travel and go back to 1960
1960 - still age 25 - grab your granny
Asking who came first in this scenario (no pun intended), you or your grandfather, is like asking where the beginning of a circle is.
You would be absolutely fine being there, but being your own grandad is impossible because at the point of conception of your Father you simply don't exist.
In terms of time travel, who came first is irrelevant
