Thank. Quite a mixed bag of replies. I think I will try both options and see what the pics come out like.
Don't go looking for a reduction in sharpness with a filter on, because you probably won't see anything (unless it's a rubbish polariser on a long lens).
The image degradation problem with filters is flare and ghosting. If you want to see that in action, the easiest way to provoke it is at night, with bright lights against a dark background - street scenes, car headlights, that kind of thing. You can also get it with sunsets.
A good test is a security light (because they're usually very bright) against a black background, with the light just off centre. That will provoke a big reflection off the sensor, which then bounces back off the rear of the filter and reappears as a ghost. You won't see it in the viewfinder, only on the actual photo, or when using live view. Put it on live view and as you move the camera around you'll see the ghost floating about. Even without a filter you will probably get some kind of ghost in that situation, as the bright light bounces back off the rear of the lens. It's unusal, because the rear of the lens is curved, but if you're unlucky with the angles you'll see something.
Coating reduces reflections a lot, and multicoating is even better. Another thing worth having is an 'easy-clean' surface which some top end filters have. A lot of the time dust etc just falls off it with a blower.
In normal use, you wont see anything amiss when you use a filter, but if you know the warning signs they're easy enough to remove. On the other hand, unless there's a real danger of something nasty likely to hit the lens (eg sea spray is horrible stuff) then a lens hood is usually all you need for protection. The lens surface itself is more robust than you perhaps think, and meant to be cleaned now and then. I use a blower to get most stuff off, and a soft lens brush. For finger marks etc, which can cause horrendous flare any time anywhere, gently rub the surface with a microfibre cloth.
And don't get paranoid about a few specks of dust - you will
not see them in the image and they are quite harmless. If you can see dust in the viewfinder, it's on the focusing screen above the mirror. If you see specs on the image (usually only visible at high f/numbers) it's on the sensor. Dust on or in the lens is so far out of focus it's invisible.