I would have thought the Jade Falcons. Especially, as the Vipers would be next given their inability to understand or get along with IS populations.
The thing to remember there though is that it sends the wrong message to wipe out the Falcons. A few years earlier, absolutely. A few years later, good case to be made. But at that point? No.
Thing is, Bulldog/Serpent was an attempt to not just wipe out a Clan, but to send a strong message. That the Inner Sphere, united, can take your most powerful force and wipe the floor with it. Why? Because that's how the Clans work- might makes right. So you take the most powerful target and take it head-on, and show them with their own logic that you are not to be trifled with.
So who do you go after?
+The Bears and Wolves sit with occupation zones flanked on both sides by other Clans, so if your gamble doesn't work and the other Clans jump in you're surrounded on all sides.
+The Bears are at this point pretty staunchly Warden, so taking them on isn't really helping anything. The move to the Inner Sphere isn't known yet, to be fair, but that political leaning means they're a bad target.
+The Wolves are split in two, with the Warden side being allies to the cause- going after their former brethren in the OZ could sour the relationship with the Wardens, even show them that the Inner Sphere can't be trusted at all- and that could have ramifications with other Warden Clans, perhaps even leaning them the other direction. They also have a problem similar to the Falcons (more on that shortly)
+The Sharks are at this point not selling weapons yet to the Inner Sphere, at least not openly, but they also don't really have IS holdings at this point. Wiping them out accomplishes nothing.
That leaves us with the two 'outer' OZs, each of which has two Clans living there. In both situations, the two don't get along particularly well. The Cats proved willing to not only stay out of helping the Jaguars, they even joined in- it's unlikely in the extreme the Vipers would have done the same against the Jade Falcons.
But that leaves us with one more important point. Remember,
MIGHT MAKES RIGHT in Clan society. In 3050, there's a case to be made for the Falcons being the mightiest of the Crusader Clans- if the Jaguars are a tie with them in terms of raw military force, the Falcons take a hefty lead with their more robust economy. But by the time we brew up Bulldog/Serpent, the Falcons have had a rough go of it. The Refusal War put a serious hurt on the Falcons, losses that weren't made any easier by the failure to absorb the Crusader Wolves afterwards (thanks, Vlad). The lash-out by Marthe Pryde at Coventry was a bold statement that her Clan wasn't as wounded as it looked, but that they took the hegira option and withdrew only underlined the fact that the Falcons were still very much below 100% strength. (That they rebuilt as they did in time for their part in the Civil War is very interesting, but at this point off in the future still)
So. You have two real options. Jaguars, who haven't really had any major conflict since Tukayyid and are at full strength and raring to go, or the Falcons, who have had their noses bloodied a few times recently. Going after the Falcons tells the rest of the Clans that you'll jump on an already-wounded opponent- and shows them that the Inner Sphere's nations are nothing but jackals who will take opportunities, but are afraid to fight a healthy Clan. But the Jaguars? This Clan is at full strength, the losses from the invasion, Tukayyid, and such are long since made up. Hell, they're readying an attack on the Combine, even! (The knowledge of that, and of the Jaguars' lack of resources back home, is likely unknown to the Inner Sphere, to be fair)
The Jaguar choice, then, is clear. You take on a Clan at full strength rather than a wounded animal. You take on a Clan that wouldn't have their roommate in the OZ jump in on their behalf. You take on a Clan that, if they talk the others into helping, won't leave you cut off entirely from help. And you show the Clans in-general that you're a serious opponent. I'm not sure, in 3059, if wiping out the Falcons would have accomplished those goals.