Inner Sphere:
Light - Jenner (highly mobile, plays well in most era's, a great harasser / flanker)
Medium - Phoenix Hawk (Maybe it's some Macross nostalgia, but it's always been a solid skirmisher in my games)
Heavy - Crusader (I have a soft spot for the Warhammer too but the squishy leg armor costs it. The Crusader is just a beefy tank that does well at any range and manages to consistently punch above its weight).
Assault - Nightstar (2 gauss rifles and a PPC are a nice way to say 'hello'. Plus I remember first reading its description in the 3058 book, where it said the Star League built them to escort Marauders. Yes, those poor little helpless Marauders ).
Clan:
Light - Puma/Adder (This little beast has obscene firepower in all of its variants. If I'm on the opposing team and I see one, it's getting an alpha strike!)
Medium - Goshawk/Vapor Eagle (It's a bit heavy on the cheese with its Targ Computer and Pulse, but I probably like it for all the same reasons I like the Phoenix Hawk; mobile, a solid skirmisher. I find it usually gets underestimated a lot, more obscure and not as flashy as the OmniMechs).
Heavy - This categories hard. The Clans have so many signature Heavy Mechs, and who doesn't love the Mad Cat/Timber Wolf? But I'm going to go with Cauldron Born (Primary config is just so-so, but the "A" with it's Ultra-20 and 2 ER Large lasers carries some brutal firepower. Just watch your heat!)
Assault - Daishi/Dire Wolf A (3 Lg Pulse + Gauss Rifle; unlike many other configs, this one doesn't overheat, it just delivers consistent high-damage)
For fun, I'm adding the <optional> Vehicle category, since I tend to feature them a lot (sticking with Inner Sphere only here)!
Light Vehicle - Saladin (speed matches the Locust but it packs an Autocannon 20. "What back armor?")
Medium Vehicle - Drillson (for a hover tank, this thing has a lot of armor, speed, and firepower)
Heavy Vehicle - Manticore (Great support tank with it's PPC and LRMs)
Assault Vehicle - Shrek (Having the firepower of an Awesome without the overheating sure is fun, especially in 3025 era games. Replace with the absurd triple-Gauss Alacorn if you're going up against the Clans!)