Always adjust the neck first. You want it fairly straight with just a bit of relief. Fret the 6th string at the 1st fret with your left hand and 17th fret with your right. You should see a small amount of relief under the 6th string at the 9th fret. I'd say about a business card thickness, even less if you like. Just make sure you don't go beyond straight and actually back-bow the neck. Only use a 1/4-turn at a time with truss rod adjustments. A little goes a long way.
Once the neck is adjusted, then do the action. Adjust the bridge saddle height. Setting the saddles real low for a low action means the allen screw will stick up above the saddles, and yeah, they can be uncomfortable for your right palm. You can replace them with shorter allen screws if it bothers you too much. You could probably find them at a good fastener supply store or online.
Lastly, do the intonation. Tune each open string and then check the note at the 12th fret. If it's sharp, adjust the saddle away from the nut. If it's flat, adjust the saddle towards the nut. (Adjust, retune, and recheck. Repeat until it's perfect. Set the intonation with new strings so it's accurate.)