This is a huge topic!
Registration depends on many factors, in rough order some of these being:
1. School of composition (eg Bach vs French baroque vs French romantic to give just a few cases)
2. Organ being used
3. The piece itself
4. What the player is trying to convey (maybe this should even be first!)
5. The player's personal preferences (some like warm principals, others like beautiful flutes etc)
1. Being Bach, there aren't many prescribed registrations like there would be for the French baroque or romantic schools. So there's no registration formula, although some pieces are prescribed eg Pro organ pleno, but not for this particular piece.
2. Arlesheim is an organ somewhat between the "south German" and "French" baroque models. There are probably quite some quite vocal stops in this type of organ.
3. Ich ruf zu dir is described by Wikipedia as being "a supplication in time of despair." F-minor is a key often reserved for this sort of piece in baroque times.
The left hand reminds me of a violin or cello ("imitatio violistica"). The bass is "gently pulsating" in a style that could also be emulated by a cello or double-bass in a baroque orchestral or chamber piece.
4. I would try to convey this sense of supplication using some vocal registration.
5. I like vocal principals, so perhaps the solo on the Principal 8 of the HW with the left hand on another manual's 8' stop. Choose pedal stops to balance -- a somewhat vague phrase that I would use to mean 16+8, sometimes +4 or more stops including reeds so that the total volume and pitch doesn't interfere with what's going on in the manuals. In this piece just 16+8 flues would be appropriate.
Now, I mentioned that I like a vocal sound, which is especially applicable in this piece. Playing a principal or octave 4' an octave lower can work for this. On this organ, you could try this on the RP and then use the Pr 8 of the HW for the accompaniment. In the Church itself this might work because the RP is closer to the audience. Or you could draw Pr 4 and Flute 4 for the RH.
Then try any of the above registrations with the tremulant(s), also highly appropriate for this style of piece.
Other things you can try:
RH solo on RP flutes 8-4-2.2/3, LH HW Pr 8
RH solo on RP Cromorne 8 with tremulant, LH HW Pr 8
Good luck!
Cheers,
Colin