Depending on where you are, in Asian countries, they tend to use A4 sized paper as full sized flyers, while in North America, it's more Letter sized paper... As for dimensions, I only know Letter is 8.5" by 11" and letter is about 2 centimeters skinner, and 2 centimeters taller...
Most of the flyer work I've done has been 1/3 A4 size as above (commonly known as DL). This allows the printer to fit 3 flyers on each page.
I guess it depends what you want to advertise. Not many flyers are going to be A4, unless you've got a lot of info to present or it's going to be printed on paper rather than card, and folded into a leaflet (A few thousand on A4 on card is going to be quite pricey).
If you're going to have them professionally printed your first step would be to find a good local printer and look at their pricing for quantities in different sizes then work out the optimal size and price from there.