When you check the neck relief capo the first fret as you did then hold the E string down at the fret over where the neck joins the body. Check the gap between fret and string at the 7th fret. Others will suggest other frets. I usually go for a gap of about 0.30mm which is about the thickness of a business card.
As for string height (action), that is a very personal thing. If you like digging in a higher action might be best. Lower if you are a gentle player. Remember though, the higher the action the more you'll have to adjust the intonation. When you fret the string you are stretching it. Tune the open string to pitch. Pick the harmonic at the twelfth fret and then fret it and pick it again. If there is a difference in tuning the intonation needs adjusting.