Which anchor rope? Nylon,polyester,double braid?

Good quality (Donaghys for example) nylon 12mm, nice & stretchy, easy to splice, easy on the hands

I use double braid. Nylon would be best but the braid falls into the anchor well and there is no need to fiddle about laying it the correct way. When its wet it just lays nicely either way and is unlikely to pick up and tangle. Nylon multi plat would be nice.

OK, been through this a few times (need to keep a copy!) but here goes.

Firstly don't use braided ropes for anchor or dock lines. If you look closely at the lay of braided ropes it is at 45deg to the line of the rope. This causes chafe (have a look at a marina at all the big boats with their black braided lines and see how fluffed up/chaffed they are). It also causes heat and noise. I have sat against a wharf with a little swell with a braided line running through an S/S hawse and it squeeked all night!!

OK, so in twisted ropes, which the lay of the strands is in line with the line of the rope.....
8 plait is far better than 3 strand because it doesn't untwist but is a bugger to splice. 3-strand is fine though.
I find nylon shrinks over time (when it gets wet/dry) and makes the rope go hard. This means it tangles easier in the locker and is almost impossible to re-splice after a year or so (I've tried), so if you stuff bit of the rope the whole length can be a throw away. Nylon can also get hot, I have known it to break (melt) in hot environments when used as a mooring line that moves a bit in the swell,

My preference is for 8-plait polyester like this http://www.deckhardware.com.au/-categories/rope_cordage/liros_mooring_lines/liros_squareline_pes_01047/
It stays soft, has a nice amount of stretch and grips well in winches.

My 2c, if you want a price on the stuff in the link, let me know. Got lot's of cruising guys using it and they love it!!!

A bit off the subject...

Is that a horse on your yacht Rumblefish?????