Armsman-

It’s like the base perk for Two-handed, or for any of the spellcasting trees.  If you use the thing, you want the perk, all of it, and now.  End story.

Fighting Stance-

As with Champion’s Stance, this will go a long way towards making you more efficient in combat.  Power attacks are always nice, especially when your opponent is blocking, and anything that eases the load on your Stamina is a good, good friend to you.

Bladesman-

Again- improving your critical chance with this isn’t as effective as the overall damage boost from the base perk, so you should always take that base perk first if you can.  That said, it’s still a nice boost and can produce strong sudden damage swings often enough to be worth taking.  This is doubly true if you dual-wield swords.

Bone Breaker-

As with Skullcrusher, this does nothing to enemies that are not actually wearing armor.  Worth having a spare mace (or pair of if you dual wield) for heavily armored enemies that you don’t have to worry about upgrading as much, but only if you were going to have the spare perks to take it- this just isn’t a priority, really.

Hack and Slash-

The damage here is more significant if you’re dual wielding since it cares about each hit, basically giving you a free poison damage effect without occupying your weapons’ poison (and without requiring reapplication after each hit).  Probably not worth the perk when you’re using sword-and-board (axe-and-board?) as your combat style.

Dual Flurry-

This is your basic dual-wielding perk, and boy is it ever useful for that.  With both points in, it’s going to increase your overall damage by about 1/3 (slightly more, even).  Particularly impressive when you consider that with two weapons, you can already expect to deal twice as much damage as someone toting around a shield, and usually about 1/3 again as much damage as someone wielding a two-handed weapon.  The first point of this is comparable to a point in Armsman for dual-wielders, and the second is almost as good as another point into Armsman.  Definitely a must-take for dual-wielders.