you need 110 volts on one side of xfmr, which will be installed through one of the knockouts in your panel. On the other side of the xfmr will be where your 12 volt wire connects, then run that wire any way you want to the doorbell chime.
I've always liked the wireless ones myself, no fuss
Depending on the mounting provided, you might find it easier to attach the transformer to a junction box rather than directly to the panel. You can install it anywhere that is accessible and where you have 120 volt power although there aren't many places you can install it without its being unsightly. Junction boxes can be attached to panels using nipples as opposed to wired in with a short length of Romex.
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.