I don't think of myself as preferring the comedies, but I guess they make up half the list. But it feels like a very balanced list to me, and I wasn't that deliberate about it. I have three tragedies, three histories (and not the histories that easily fit the tragedy mold), three comedies that actually fit a modern conception of a comedy, and then Merchant of Venice and two "late Romances."
For worst plays other than Timon:
I agree that Two Gentlemen isn't very good, mostly a template for better plays. It has the classic bit with Lance and Crab and a really wtf ending, other than that it's pretty forgettable, and the texts has some obvious signs of rewriting that were never smoothed out. That's probably the one that I would be least excited to see, although the filmed RSC version is good.
Merry Wives has some funny set pieces but I've yet to be convinced that it doesn't need some judicious cutting to play really well.
King John starts of well but I get bored in the last couple acts. I've seen the Startford version before, somewhat recently actually.
Henry VIII has some good characters but to me it's still mostly a museum piece. Peter Saccio makes a good case for it in the Great Courses lecture on it in the "Shakespeare: The Word and the Action" course. But while that makes me respect it intellectually, I'm still not a big fan.
I disagree with lumping the Henry VI's together. I think Pt. III is great and is a contender for the most underrated Shakespeare play. I like Pt. II well enough but it's a lesser work. Pt I has some colorful characters and enough action but it really isn't very good and was probably written as a cash-in-prequel.
Of the other plays most likely to get crapped on:
All's Well is not one of the better plays IMO but at least its problems are interesting problems, it has good parts for actors, and the subplot is funny.
Measure For Measure is very good although very ending is difficult to interpret, and I mean that in a bad way.
The first two acts of Pericles don't read well but they can play well and the last three acts are good. I saw a wonderful production of this, and it ended up being only one of two plays that I saw live before I saw it on the screen, so that helped biased me in favor of it.
Titus isn't one of the better plays but it can be very entertaining. I've seen three filmed versions and liked them all.
Two Noble Kinsmen is good enough overall, and the Jailer's Daughter is a great character. I enjoyed the Globe production.
Troilus and Cressida is interesting but it's probably one of the least marketable.
I think everything else is pretty canonical. Comedy of Errors has more naysayers than most of the rest and I do think that one is a lesser work but it can be fun. I haven't seen it in person but I think it's produced more often that many of the better plays. It's short and I'm sure it's one of the easier ones to take the kids to.