Choice 2.
You are a courtier, naturally skilled in courtly business and diplomacy. Put it to use; reputation from a successful negotiation with the Turks is very useful in the diplomatic world - you will look like an emperor that is doing his job, and, if succeeded, do it well. Your army and your generals (or at least most of them) are loyal to you, at least for now, and would be willing to fight the emperor's wars for him. You are still young [historically, Michael actually ruled (incompetently) later only after Diogenes had lost the battle of Manzikert] and other wars can be fought later on. The Turks are a warlike people with clans traditions, and the Sultan will respect more an emperor who's respected him enough and brave enough to "show himself." In fact, will the Sultan be offended if he feels that you're not considering him worthy enough that you just send a letter and went on to another campaign instead, against "petty" raids by the "petty" nomads?
As for the Bulgarian situation, I'd rather send Manuel, your most loyal general. Time is not of a concern in Bulgaria, but rather how complete the job is done, and that tax shipment, if recovered, could at least help ease the financial troubles. I'd rather have Crispinus continues to hold on to Bari; an Italian foothold, if lost, is going to be very hard to get back. Bryennius' plan require too much force; it may affect your upcoming diplomacy with Alp Arslan if he realizes your empire's forces are occupied elsewhere. Just look at the modern world: North Korea goes on showing the middle finger on the US and Iran becomes a rising star on the world stage now that the US' hands are tied in Iraq.
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