One thing to consider is what you're tying up to. Double-braid lines tend to get the outer braid picked apart when used on rough wooden pilings, far more so than three-strand nylon docklines. If you generally tie up to wooden pilings, then use three-strand, otherwise use whichever you prefer. Three-strand line tends to hockle if you're not careful, but often has better chafe resistance characteristics than double braid line.
You shouldn't use polyester for dock lines, because it doesn't stretch as much as nylon does, and as such can cause much more damage due to shock loading, as seen in Natotm's post.
For anchor line, I would recommend octoplait, since it doesn't have the problems with hockling like three strand, and it tends to flake in the anchor locker more compactly, since it is more flexible than three strand usually is. It also makes a good chain-to-rope splice that will fit through a chain/rope gypsy well.
If chafe is a big problem, you should use spectra/dyneema chafe protection sleeves. These are better than rubber or plastic hose for one major reason. A majority of dock line and anchor line failures are due to the nylon heating up due to internal friction as the rope works, leading to the rope melting and failing. Using a woven chafe protection sleeve allows water to get in to the rope and lubricate it, helping prevent internally generated heat and related failures.
Rinsing out your docklines once in a while is also a really good idea. This can help get rid of any embedded dirt, which can damage the rope fibers as it works its way into the rope.
As for sizing the line—going too heavy on the line is also a problem—since it won't stretch and absorb the shock loading of storm surge and such. 1" dockline is too heavy for most boats 35' or less. You want the boat to stretch the line rather than shock loading the deck hardware the line is tied off to.
Another problem with using lines that are too thick is that the cleats probably won't deal with them well. A good rule of thumb is that you should use docklines 1/16 the size of the cleat in diameter. If your boat has 10" cleats, then the largest dockline you should use on the cleat is 5/8" rope. This allows the cleat to easily handle two docklines at a time.
as the lines held tight; thankfully, they didn't break loose and damage any boats. Several marinas to the west of us were literally washed out into Lake Michigan. Boats and slips broke free and became a floating battering ram.