I generally avoid using filters unless there's a compelling reason for it.
If you do use a filter, get a high quality filter with good anti-reflective coatings.
If you look at the filter and you see a reflection, then that means two bad things are happening...
#1 the filter isn't transmitting all of the light. You're losing a percentage of it (possibly a pretty good percentage of it). It isn't possible to see a reflection unless light is being reflected... which means that light is not going through the filter.
#2 such a filter will cause "ghosting". It's a nice flat surface. So what light does pass through can reflect off the front objective element of your lens, back onto the filter... and that nice "flat" surface of the filter will reflect the light back again into the camera and you get ghosting.
All glass is reflective. All filters have lens flare. It's not a question of "if"... just a question of "how much" and is it enough to notice. When you have a bright point in an image that also has lots of dark or shadow areas, it's possible for the ghost reflections of those bright spots (e.g. street lights, the moon, etc.) to show up as ghosts in the dark shadow areas.
Here's an example:
On the left is the inexpensive Tiffen UV filter. On the right is a B+W brand filter that has high quality anti-reflective coatings.
I've placed a piece of black card stock on the table. Out of the frame is a desk lamp.
Look at the at the B+W filter on the right, it almost looks as though it's just the black filter ring with no glass in it. There is glass there... but that filter has high quality anti-reflective coatings... so the light passes through almost as if the glass isn't there. If you look at the color of the black card stock behind the glass ... and compare it to the black card stock where there are no filters at all... the "black" is nearly the same.
Look at the lower quality UV filter on the left ... which does NOT have quality anti-reflective coatings. Notice how you can easily tell there is glass in the filter and that the black card stock looks a bit washed out ... it has lost contrast.
What you can't tell in this photo is that when I'm holding these filters and tilting them, I can easily see reflections in the Tiffen filter. I can technically also see reflections in the B+W filter... but they are very dark/weak reflections that aren't easy to see.
This is one of those "you get what you pay for" things.
Even though I own filters with quality anti-reflective coatings... I would still get reflections/ghosting (albiet very faint) using the filter.
For this reason... if I don't have a compelling reason to use the filter, I leave it off the camera lens.
