Mechwarrior 2 mercs was I think the better single player as far as the missions were concerned. Story-wise Mechwarrior 3 was also pretty weak since the smoke jaguars were fighting against you with IS units and whatnot.
Yeah, in MW3 you were only a clean-up party after operation Bulldog, on a non-canon planet. Pretty boring. MW2:Mercs was awesome because you sometimes even fought in canon battles. Even regular MW2 was nice in that department, since you at least fought on canon planets and were able to follow the canon story in the mission briefings and de-briefings.
The Basic events of MW3 on Tranquil happened in B-tech canon, and Tranquil is a canon world (
Trial by fire is a canonical story of this event). Also the basic out line of what happens in MW4 is also canon (the FC Civil war source book mentions this).
Mechcommander 1 also has some elements make it into canon, the MC interface for instance is canon (imminent crisis mentions it, and it's success in bull dog)
Ghost Bears legacy also has some canon elements (IIRC their is mention of Clan Wolf behind a raid on a Ghost bear facility), as is the old crescent hawks series has some canonical elements (like the main character and his mech)
The MW3 expansion I do not believe is canon, and I do not know how canonical the expansions of MW4 are as well. Mechwarrior 2 is not exactly canon either due to it's plot outcomes, and I do not know how canon is Mechcommander II is. MW2 Mercs is not canon either but as your one of the countless small merc units you can easily be present for some of the known events but details would be different.