The only thing that is required is that you field at least 1 HQ and 2 troops from your 'main' list. Then you can include the previously listed types of units from the allied list.
And for inquisitors, you'll indeed have to decide wether they are a WH or DH inquisitor, and pick their retinue + wargear from their respective codices. On another note, this also goes for assassins. If you have a WH Inquisitor, you'll need to field your assassin from the WH force, if you have a WH inquisitor, you field one from the DH force.
Since you only have 1 Elite slot, this means that unless you field an allied force HQ inquisitor lord, you can't put an allied assassin in your force.
While if you field your assassin from your main force, you can use a 2nd elite slot or an HQ slot for your inquisitor ( or inquisitor lord ).
As for choosing which ordo will be your 'main' force, and which one your allied force, I would recommend looking at the Heavy Support slots. What can demon hunters field as heavy support that you'd really like, and what can witchhunters field.
I think something along these lines would work well:
Main force WH
HQ: Cannoness, jump pack etc.
2+ sister squads
Fast attack: 1 x seraphim
Heavy support: Excorcists x 3
HQ: grey Knight captain with termie retinue
Elite: Inquisitor with mystics and a LRC
some Grey Knights.
Deepstrike your GKs and your termies, jump ahead with seraphim and cannoness,
hold your basic sisters back and have them rain bolterfire on the enemy, and defend the excorcists and inquisitor.
Use the LRC as center piece to block enemy light of sight to your excorcists and sisters in the back.
The inquisitor with the mystics are there to intercept incoming deepstrikers, and give the sisters the ability to give them a taste of close range bolter/melta fire when they land.