Going from my experience as of late:
The Black Jack may be rare in the pug queues, but it's pretty common on the IS side of CW in the form of the 1-X (and the rare, 3x Large Pulse Arrow). Very, very good medium for the tonnage and the (current) quirks on the 1X, with some fairly solid other variants (nothing wow worthy, but that might be why they're uncommon). You don't tend to see its brethren very much however. The Blackjack just doesn't seem overly popular despite some pretty solid load-outs.
If you want a fairly unpopular mech that still performs well, definitely a good choice on the IS side right there, and probably what I'd recommend for a true underdog. It hasn't hit its full stride of acceptance despite being a nasty little poker. I'm actually a bit surprised at how little I see them around compared to Hunchbacks.
The Treb just... isn't that great. Between the size, the fragility and the load-outs its less of an issue of being unpopular so much as just... not good given the alternatives. See them here and there but fairly rare just due to being pretty damn bad. They're in desperate need of a rescaling.
I see Vindicators so infrequently I rarely even -recognize them- when one pops up. Very unpopular, very rare to see on the field. The only other mech that I've seen about as rarely is the Anansi hero Spider, but you still tend to see other variants here and there. Vindicators? Rare bird indeed, they just don't tend to pack the punch that other mechs do with similar speeds etc. I can honestly count on one hand since last year how many I've seen in matches.
Highlanders also tend to be very rare for something beefy, but they suffer from the same issue as the Victor and (another now very rarely seen) the Shadowhawk; they were beasts during the poptart meta, but once that get dialed heavily back their spotlight stealing as some of the kings and queens of mechs also sputtered out without finding another niche to weasel into.
Their claim to fame was primarily just that; popping up via previously stronger jump jets, popping off a quick blast while dropping down. You still get some pop tarting going on but their niche long since passed on by. You're more likely to see a Cicada or Shadowcat doing that nowadays along with jump lights. I couldn't recommend the Hawk Victor's or Highlanders currently; they're not so much underdogs so much as bygones of a past meta.
On the Clan end I tend to see a bit more Summoner use (usually PPC+ Gauss neo-poptarts because, well they don't seem to do much else that others pull off better) than previously, still see even the "******" clan lights, hell, even the occasional Gargoyle and Ice Ferrets. They don't seem to entirely drop off the radar even at my tier like some IS mechs do.
If I were to edge towards a Clan underdog, it might be the Nova (rarely used, but with some nasty niche builds) or the Shadowcat (**** upon for a lack of energy hardpoints, but a solid poptart/hyper mobile medium with a few decent, though not insane loadouts if you capitalize on that mobility); hell the SCAT has ecm to boot, though the MASC doesn't add much to it (still a bit unique though).
If something big and beefy, the Executioner gets crapped on a -lot- but it has some very punchy loadouts, some hidden gem setups (a light hunting assault? Doable given masc turn rates etc. if they think you're easy prey and come to get ya; they usually do too the poor ********) and still manages to be a rather mobile assault in general. Like a Blackjack it has some builds that are considered pretty good, but you don't tend to see them frequently. They don't have quite the same level of problems as Gargoyles either with the potential to build something "metaworthy" if you really want. Also... Masc. It's the only mech right now that -really- capitalizes on it's use as a great addition. Also, the Phranken camo spec looks badass on them.
I wouldn't bother with the Myst Lynx currently despite a lack of popularity; it's just not that great much like a Commando and some of the Spiders. Some skilled light pilots can be -vicious- in them, but it's less of them being an underdog and more of them just under performing and being rare for that reason. They jump like mad, they're small, but their hard point placement and lack of speed just makes them entirely obsolete in any respectable way to a ACH. The Kitfox isn't in much better of a spot, though the Adder at least can pack a hefty punch for its size.