If you're just curious about ConLangs in general, just about any one will do.
The most useful fictional-world languages are KlingonLanguage and QuenyaLanguage; they can provide a basis for communing with fellow fans. Some great works have been translated to KlingonLanguage, and in Star Trek 6, the Klingons claim Hamlet is best when read "in the original Klingon."
If you'd like to communicate with non-geeks, EsperantoLanguage is probably your best bet for the widest pool of speakers, compared to any other ConLang at least.
LojbanLanguage is probably best for language theorists. It seems quite different from most other human languages, particularly Western ones, and doesn't have as broad a social support base.
Other conlangs with (a small number of) actual speakers include [TokiPonaLanguage?] and VolapukLanguage.
See also PrivateLanguage