The Gemara (Rosh Hashana 26b) says that any type of horn is valid for a Shofar, be it a ram, a gazelle etc., but that a ram is preferable because its horns are bent, much like someone who bends over in prayer. Rashi (ibid.) says that a ram’s horn is preferable because it is a remembrance of the ram that Avraham Avinu slaughtered in place of his son Yitzhak. in the same vein, the Shulhan Aruch (Orah Haim 586:1) rules that, although different types of horns are valid, the preferable way to fulfil this Mitzvah is with a ram’s horn.
Interestingly, the Rambam says that only a ram’s horn is valid for a Shofar. The HIDA (Birke Yosef § 586) explains that if one does not have access to a ram’s horn, one should not make a blessing over other species of Shofar. For example the horn commonly known as the Yemenite Shofar is a long ibex’s horn. Rabbi Ben Zion Abba Shaul (Or LeTzion vol. 4) says that if a Yemenite Shofar will be used, that at least the first thirty blasts should be from a ram’s horn.
Summary: The ideal way to fulfill the Mitzvah of listening to the Shofar is with a ram’s horn.