The proconsular command to fight the eastern war was the most coveted command in a generation. It was the cause of the first Roman civil war because the most popular and glorious politician and general of the time (Marius) decided to snatch it away from one of the best Roman generals who enjoyed wide support among the optimates (Sulla).
So it is almost impossible a second rank politician like Sertorius, without noble ancestors and extremely strong support, will get the command of the war against Mithradates.
I poorly worded "my vote" would go to Sertorius. I actually meant he would be the most effective general IMHO sans Sulla that I would personally choose to send.
You are completely correct to point out that it would be nearly impossible for him to get chosen. He was considered way more of a hayseed to the Roman Patrician/Senatorial Class than the looked down upon Marius. For that same reason I don't think its possible that Pompey Strabo, a very competent if not particularly beloved by his own troops, would have gotten chosen (though I could be wrong, he was elected Consul once). His son, building on the father's legacy, was looked down upon by the Optimates until they had no choice but to need him.
Now if whoever gets sent to Greece first gets crushed. And the next guy gets crushed too; then, much like with the Cimbri/Teuton invasions and the patricians holding their nose to elect Marius Consul again and again and again, it might be possible for an effective general from a second rate bloodline to get lifted to command. But even with multiple crushings, Mithridates, as he is not directly invading Italy, isn't the same sort of perceived existential threat to Rome as the Germans were a generation before. So they might just keep running through bloodline acceptable commanders until they get a decent one or a lucky one.
As for who's the best combo of generalship and requisite political juice to be a feasible pick for gaining command initially in Greece ....
For the Optimates ... I'd be forced to go with ... Metullus Pius????
And from the Populares side ... damn, its really, really hard to pick anyone but Marius, who hovers over this side like a giant until his death ... who the hell would he choose to go in his stead, that is probably who it would boil down to ... a tag team of Cinna (as co-Consul) as political lead of the expedition and Sertorius as who ever damn legionaire understands is actually in charge of the fighting?????
If the war dragged on and the Populares had the Consulship, I guess at some point, assuming he isn't killed, you'd have to think Marius the Younger (who was voted Consul in like 84 or 83) would be a Populares candidate. An outside the box idea might be a surviving Marcus Livius Drusus (can his survival be butterflied somehow by the non-existence of Sulla???) against Mithridates ... but that would likely butterfly the Social War entirely. Which would likely mean that Livius Drusus has nearly all of Roman Allied Italy more or less as clients of his; immediate First Man in Rome status for near as long as he lives I would guess.