I received a warrant of arrest letter for an unpaid citation for speed exhibition, what are my options?

You can no longer simply pay the fine. To handle a warrant, you must turn yourself in to the issuing court, with or without an attorney. You'll try to negotiate a recall of the warrant[s] and negotiate a plea bargain on any Failure to Appear charge. You'll try to negotiate bail reduction or OR release. You'll try to negotiate a plea bargain or take to trial the outstanding charge that caused the warrant. On misdemeanors and infractions, your attorney can appear in court without the defendant being present. Effective plea-bargaining, using whatever legal defenses, facts and sympathies there may be, could possibly keep you out of jail, or at least dramatically reduce it. Unless you're competent to effectively represent yourself in court against a professional prosecutor trying to put you in jail, most people hire an attorney who can.

Exposition of speed is an infraction. Failure to show is a misdemeanor. If you show up in court ASAP you may get the misdemeanor dismissed.

This is a misdemeanor. So there can be jail and or fines. You will either have to post bail and appear, your appea rance can be done by an attorney, or you will have to go to the jail and appear in court in the afternoon or the next day if you do not turn yourself in early enough.