I'm at a crossroads at the moment. I'm trying to decide what second weapon to buy, because even though I love my flourish, it does so little against constructs and jellies that I am just not contributing. Now I have to ask, which would be more effective: gun or second sword? I'm not a fan of bombing personally.
And to add on, is it better for a character to specialize completely or is there something to be said for versatility? Best combos?
Honestly, there is no RIGHT answer, it depends on what you enjoy doing. Personally, I have 3 swords, one for each damage type, and an elemental gun for switches/pesky constructs. If you love your flourish, I would recommend either an elemental weapon (then you'll get something doing good damage to constructs, and acceptable damage to slimes) or a normal damage weapon. Shadow would be fine, but most people find constructs to be more dangerous than slimes, so it is less of an issue. The elemental brandish lines or alchemers would be the most obvious choices for elemental, and calibur, cutter, and blaster are the more common for normal. End game having a mix of damage types like I do is useful, but not required.
For spec/versatility, I think pure specialization is not worth it. Specing in swords, particularly, can get you dead a lot faster when you don't have that back-up gun or bomb to finish off a mob when at low health, or deal with that out-of-reach gunpuppy that's happily shooting you down. It can be done, and quite well, but once you have a weapon of each damage type, there is much less incentive to toss your 4th. If you only want two weapons... yeah.
Again, this is all personal opinion, so take any advice with a grain of salt.