They can either be wood or aluminum. I encourage you to use a wood one. If not, I will make fun of you like I do my good friend Bill Booker at LaSalle-Peru H.S. for using his aluminum one. If you choose the wood fungo, I would recommend taping the barrel. If you hit a good number of fungoes, the tape will increase the durability of the bat. I took the tape off of one once. The barrell was like sawdust, but I re-taped it and it was ready to go. One season, I figured it out, between the high school, American Legion, an junior high seasons I had hit over 10,000 fungoes. Tape it up!
The bat's form has become more refined over time. In the mid-19th century, baseball batters were known to shape or whittle their own bats by hand. This allowed there to be a wide variety in shape, size, and weight. For example, there were flat bats, round bats, short bats, and fat bats. Earlier bats were known to be much heavier and larger than today's regulated ones. During the 19th century, many shapes were experimented with, as well as handle designs. Today, bats are much more uniform in design.
First base fungo hits fly balls to center field (helps here if both fungo hitters move up and apart, hitting from about the front of the mound extended towards the bases). Center throws to second, second baseman is cutoff (for us it was, anyways - change to suit your style). Third base fungo hits balls to left field, who throw to third, with a second shortstop as cutoff (but you really don't need one, if you're shorthanded).