I would throw the horseshoe preserver / lifebuoy to the MOB before going to the
GPS: the buoy will help the MOB to stay afloat, that's #1 priority. If I'm alone on
deck, I will not even bother with the
GPS: manoeuvring close to the MOB is more important.
When briefing my crew on what to do if I fall overboard, I tell them to try at least once to get me before sending a MAYDAY: turning the boat around takes a few seconds but sending a useful message takes about one minute.
IMO, the EPIRB is worthless in such a case: it takes too long for the alert to reach the local MRCC. Then, it takes at least 1/2 hour more (when coastal cruising) to have
rescue (vessel / helo) on the area. A PLB with
AIS is useful but it should be in the MOB's pocket before falling.
To get the MOB back on board, I prefer to have him/her on the lee side: it's much easier to pass close upwind and IME, the risk of bumping him/her is very small.
Alain