I am a firm believer in full length mudguards fitted to both the front and rear wheels: There is nothing worse or more demoralising than getting even wetter from wheel spray on a rainy day: wet up the front from the front wheel, and a soaked back and neck from the rear wheel. With the exception of my Polo hack all of our bicycles have full length mudguards fitted, Including our two full suspension, disc braked MTBs.
The only bicycle that we have that had mudguards on when we bought it was my Falcon Explorer Hybrid, and I have fitted after market mudguards to all of our other bikes.
I haven't encountered a real problem fitting them to any of the bikes, although for the MTBs I did have to change the standard screws supplied with the kits for longer socket head bolts (Allen key type) because I fixed the mudguard stays to the brake caliper mounting points. But using bolts of the right length to suit the addition of the stays and tightening them correctly will not cause any safety or performance issues with the brake calipers.
Plastic mudguards were bought by me mainly because of the price, and for ease of adjustment to accommodate tyre clearance. If you should inadvertently pick up debris when riding the plastic mudguards will flex a lot before becoming damaged, and any creases can taken out of the plastic with the use of a hair drier. Also when I was younger and riding a bike with metal mudguards I had a serious off because a drinks can be came trapped between the tyre and guard resulting in me going over the bars.
Flaps are not really essential, especially if the mudguard protrudes slightly below the horizontal centre line of the wheel, but I do like the bottom end of the front mudguards to be between the 7 O'clock and 8 O'clock position to prevent road spray coming up at me .......... I really hate this.
A few weeks ago, I obtained and fitted some additional plastic flared cups to the mudguards on two of our bikes. Unlike normal flaps theses are rigid and not flexible, and because of the slightly oversized flaring of the cups they catch an awful lot of the preipheral side spray often produced by the tyres. During the recent rainy weather I have remained drier, and therfore a lot happier when cycling.