A TRACON Controller reported they became distracted while vectoring aircraft to the final approach course and issued a late heading to base leg resulting in a loss of separation. While resolving the separation loss one of the aircraft flew below the Minimum Vectoring Altitude.

Narrative

I had just finished receiving the position briefing as I sat down I noticed North arrival was going to feed me an aircraft for Runway XX. Aircraft X was on the right down wind for Runway XX (minimum fuel). Aircraft Y checked in 6000ft. for Runway XX. The plan was to turn Aircraft X base in another mile or 2. I felt it was a little early to turn at that moment. I descended Aircraft Y to 2500 ft. and turned direct (FAF) to sequence them in front of the aircraft from the north. Aircraft checked in 090 heading at 4000 ft. I sent the aircraft direct ZZZ; a fix on their flight plan. Aircraft asked for spelling of the fix. I stated the 3 letter identifier and confirmed their routing. This delayed my base turn for Aircraft X. I noticed the conflict turned Aircraft X left 270 and I asked Aircraft Y to stop descent at 3000 ft. and turn left 030 (it was to late to say 3500 ft.) I didn't want to cause confusion or delay pilot action. Aircraft X never replied to my turn left 270 transmission. I believe Aircraft X asked about the turn and heading. I issued the 270 heading again and a descent to 2000 ft. Separation may have already been lost at this point or just about to but I wanted to increase the separation as much as possible. The 2000 ft. descent may have taken the aircraft below 2200 ft. MVA before I could go back and climb them back to 3000 ft. Separation was lost at approximately 500 feet vertical separation and approximately a mile lateral separation.Usually when I first take a position I sign on and bring up my preferred settings set (airspace map mileage for the sector and any other maps I usually use for the sector) before I start making transmissions. I've learned that even little differences in position setup can effect how your mind receives and processes the information the scope is giving you and priority of your transmissions and control instructions. I didn't do this. I sat down and started issuing instructions. I probably didn't need to send Aircraft Y to ZZZZZ and descend them to 2500 ft. the same altitude Aircraft X was descending to. I could have either descend to 4000 ft. or 5000 ft. or delayed my vector to intercept final until after I turned Aircraft X. Either would have maintained positive control and separation. I could have reached out to North arrival and ask them to slow the aircraft they were vectoring from the North to maintain the spacing for the arrivals. When the aircraft checked in on 090 heading I allowed the aircraft to distract me and delay my turn for Aircraft X.