Where to capo for Ab minor
Put the capo at fret 4 and play Ab minor using Fb minor shapes. That is the easiest of the eight positions ranked below, and it is what most players reach for. Against playing Ab minor open, it drops the mean difficulty of the key's seven chords from 5.2 to 3.4 and gains 11 ringing open strings.
You want Ab. Capo 4 and play in Fb.
All eight positions, ranked
Each row transposes Ab minor down by that many frets to find the shapes your hand would actually make, then scores the best voicing of all seven chords — fewer fingers, less stretch, closer to the nut, fewer muted strings. Lower is easier. Standard tuning (E2 A2 D3 G3 B3 E4).
What you are playing
The seven chords of Ab minor are Abm, Bbdim, Cb, Dbm, Ebm, Fb, Gb — the ones the ranking above is scored against. Their diagrams are on the Ab minor key page.