>Which kind of Ethernet cable is best for modem, router connections.
CAT5 or CAT5e. CAT6 is overkill. CAT3 is garbage and unsuitable.
For connections between devices, the more flexible stranded wire CAT5e
is probably better than the stiffer solid wire. I'm partial to
garrish colors, but that has no effect on performance.
>the cable come with fiber conductors?
No. Fiber optic networking has totally different connectors.
Different vendors use different connectors.