Fastest and most engaging class

[Kwoon]

Skill Speed in general has always been a pretty poor stat. Typically, once we get all the mathcrafting out of the way, it tends to be -hit EXACTLY x or y and forget it- which is usually more about fitting buffs/dots around a rotation or something like fitting another RA proc chance for Bard. That said OP, if you're looking for engaging your best bet is going to be relying on procs or positionals.

Monk- Lots of positionals, so fairly high movement to keep you active and engaged.
Bard- TONS OF PROCS! Especially if you stack that crit, which you should be doing anyway. The Opener has you wishing macros didn't suck because there are too many buttons to push and continues to keep you busy as the fight goes on since the majority of the time, you're upkeeping your crit buff, your dots and managing crit procs in the form of RA, Rep, and Bloodletter.
Dragoon- Haven't played mine in SB, but if its similar to how it was, there's enough positionals to keep you engaged and two of them are randomish (in the form of which one you get.)

Personally, I play Bard and find it very engaging. Doesn't hurt that you have a lot of support to offer and can tailor your rotation to fit the needs of the party for that particular fight (such as holding onto Foe's+Refresh for a little bit to line up with healer MP needs.) My crit is in the 2100-2200 range before food/buffs come into play so the crits on DoTs happen often, keeping me busy. Its also very fun in dungeons when you can use an enmity cutter and steal rip aggro from a tank due to how much damage you're putting out thanks to procs.

[ZhaneX]

Dragoon- Haven't played mine in SB, but if its similar to how it was, there's enough positionals to keep you engaged and two of them are randomish (in the form of which one you get.)

They removed the randomness, tying each of the positionals to one of the combos, and also making it so that now you follow one up with the other.

Anyway, I'll echo what others have said about Bard.
Machinist is misery itself by comparison.