Hmm. Tricky one. Will they give you the option to have mono with 1 colour? Personally, I think would look good. Sometimes lots of colour is too fussy, but mono is a bit dull. One splash of colour could be a middle ground.
What colour paper would you use if it was black & white?
I have to print them myself, or contract out the printing to someone. 1 Colour you talk about is called Spot Colour in print trade. Have used that in the past, can be very effective and is lower cost than full colour print, when large run is being done using litho. Run size alas is not large in this case, only 150 sides of A4, so I'm self-printing. Choice was to use my mono laser, or colour inkjet. Have decided upon mono laser, with very bright paper. That way, with luck the leaflet is less likely to get lost within the envelope - at least that is my hope. Now all I need to do, is design something suitable, using just black, and then print and cut to size. Reminds me of days before VistaPrint when I used to produce all my own marketing materials.
I would say it depends entirely on your design, the publication it is going in, the paper it will be on and the "feel" you are going for.
B&W can sometimes look a bit budget - colour can be too "noisey" and messy, Spot Colour can sometimes be tricky to pull off. Your webiste is very very professional (I am very envious!) so I would consider a tie in theme to the website & chose your pallet from that. The next obvious step from the flyer would be your site so it makes sense that they flow well together & keep up the professional feel.
If I were you I'd print on something glossyish & bright. The flyer I use for posting through doors is a bit mental and designed to catch the eye of the children as well as the parents (who normally bin through the door stuffs, have a look here for an oldish example if you want http://img170.imageshack.us/img170/4653/flyerexamplemu1.jpg).
I think something like this could work? http://img244.imageshack.us/img244/8043/nickmockupud0.jpg quick example but you get the idea.