Stick with
Peter definitely.
Pierce is ok, but
Piers to me is one of those 'posh', upper-class sounding names certain people use (in the UK anyway) that just sounds a little bit pretentious to me :-/
Pierce has slightly more of an edge to it, it's 'cooler' than
Piers IMO, but I really do think
Peter is the best, it's one of my favourite names :-)