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!
Versatile fungo bats are the ones tailored for both outfield and infield practice. Infield bats are effective for those that desire to rip their ball to the young ball hawks. These bats are thicker and heavier through the center in order to give you more oomph. Thicker bats work better especially to softball coaches to hit bigger balls utilized for softball.

Maple bats in particular were once known (circa 2008) to potentially shatter in a way that resulted in many sharp edges, sometimes creating more dangerous projectiles when a bat broke.[9][13] Maple bat manufacture evolved significantly, in cooperation with Major League Baseball,[11] paying special attention to grain slope, and including an ink spot test to confirm safest wood grain orientation.[11]
Manufacturers position each bat's label over the mechanically weaker side of the wood.[9] To reduce chance of fracture,[9] and maybe deliver more energy to the ball,[10] a bat is intended to be held so the label faces sky or ground when it strikes the ball during a horizontal swing.[9] In this orientation, the bat is considered stiffer and less likely to break.[11]
Fungo bats have been around since the beginning of baseball and as most of us may know, baseball was said to be invented by Abner Doubleday in Cooperstown, New York during the summer of 1839. Since fungo bats were much easier to swing and gave off a ton of pop, they were almost seen as cheating back in the day. In a book from 1897 named "The Technical Terms of Baseball," the sportswriter Henry Chadwick stated,"The weakest batting is shown when the batsman indulges in fungo hitting." It wasn't until baseball bat regulations came around that fungo bats were only used by coaches and parents. 
Baseball bats are made of either wood, or a metal alloy (typically aluminum). Most wooden bats are made from ash. Other woods include maple, hickory, and bamboo. Hickory has fallen into disfavor over its greater weight, which slows down bat speed, while maple bats gained popularity[5] following the introduction of the first major league sanctioned model in 1997. The first player to use one was Joe Carter of the Toronto Blue Jays.[6] Barry Bonds used maple bats the seasons he broke baseball's single-season home run record in 2001, and the career home run record in 2007.[6] In 2010, the increased tendency of maple bats to shatter has caused Major League Baseball to examine their use, banning some models in minor league play.[7][8]
For starters, we should clarify just what we’re talking about when we say fungo bat. Longer, lighter and thinner than a regulation bat (but a larger barrel), a fungo bat is typically 35 to 37 inches long, and weighs between 17 and 22 ounces. As David Allison wrote in the June 1978 edition of Country Journal, “A fungo bat looks to be a cross between a baseball bat and a broomstick.”