FYI - once you get new mechs/pilots an I get into the game, just wanted to let you know my mech preferences (from MW4, not sure which of them are even availlabe, my battletech knowledge is limited)
roughly in order of preference:
Found this nice shape chart:
In the order you listed them, this is how long it will take each of those designs to appear in this campaign, game-time wise.
Deimos - 85 years
Canis - 58 years
Bushwacker - 53 years
The Pitbull is not actually a real 'Mech. Sorry.
The Tenchi is not a real 'Mech either. MekTek flat out made up a lot of 'Mechs for their MekPaks.
Fafnir - 63 years
The Black Heart is another made-up 'Mech by MekTek.
Cougar - 58 years
Hellbringer (Loki) and Summoner (Thor) - 49 years
Hellhound - The one you're thinking of doesn't actually exist, and was made up for MechWarrior 4 (not MekTek's fault this time!). The Conjurer (Hellhound) kinda shares a name with it, though, and will be technically-but-not-likely-at-all available in 49 years.
I think the shortest wait on that list is 49 years. I'd suggest picking something else.