I would like to build the best all around omni-directional antenna,
that would have a good gain, in the FM broadcast band.


There are very few omni-directional antennas that also have gain. Are you using
this for a transmitter or a receiver? If for a receiver, you also need some
bandwidth, unless you want to concentrate on a small segment of the 10mHz band.
For a part 15 transmitter, bear in mind there are some restrictions on antenna
size.

I've gone through the same excercise on the 2m Amateur Radio band, in an effort
to have as wide a coverage as possible without resorting to a directional beam.

My solution, which might also work for you, was a colinear array of three
sections. You can find design information on the web or in the ARRL Antenna
Handbook. For 100mHz, a 3 element colinear would be about 8 feet high. You
could also use a J-Pole with colinear section which would only be about 6 feet
high. The colinear requires a matching coaxial balun at the feedpoint, the
J-Pole has a built-in matching stub and may be fed directly with 50-ohm coax.
The disadvantage of these antennas is that they are fairly narrow band. You
just can't get something for nothing these days. :-)

If you can't find colinear or J-pole information on the web, but this sort of
antenna looks interesting to you, drop me a line and I will direct you to
specific sources of information.

Doug Moore