Hi Adam, as Neil says above, 3-4x your regular depth is about right. In the east Wight area (the area south of Hayling Island) it rarely gets deeper than 30-35m, so if you aim for around 120m of rope you'll be fine. On my 165 I used 12mm 3 strand - generally the larger the diameter, the easier on the hands if you have to haul manually. Do you plan to use the Alderney method of anchor retrieval? If so, you can reduce your rope diameter to 10mm.
As for an anchor, I recommend you keep the grapnel for a spare and use a Bruce anchor for your main. Better holding power than the grapnel and they're not too expensive. Don't forget to trip your anchor in case of snags. Shout if you need help with how to rig an anchor to trip. For your boat a 5 or 6kg anchor would be ok. I used a 5kg on mine.
For chain the general rule of thumb is to use chain that is 1.5x the length of the boat. On my 165 I used 1x the length of chain, but went up a grade and used 8mm chain instead of 6, and this worked fine.
In fact, I have this chain going spare if you want it. 5m of 8mm galvanised chain. Free of charge but you'll probably want to pick it up in person as I imagine the postage might be quite steep. From memory you were planning to use your boat in the Reading area as well as on the coast? I'm between Reading and Newbury.