Even what she should mechanically take as a feat. Still leaning towards Tavern Brawler - even though it's dumb, oOoO, I should probably take 20 CHA instead~
It's dumb, oOoO, you should probably take 20 CHA instead.
The grappling parts of Tavern Brawler aren't even that good from a grappling perspective, and are completely useless to a non-grappler. The unarmed damage die upgrade is nice if you plan on punching people a lot, which is the real reason grapplers might pick the feat up, but if you're not an extremely punchy character it's not going to do much either.
As for proficiency with improvised weapons, you already have proficiency with improvised objects that resemble weapons you're proficient with. I mean, this is technically a "GM's option", but I'm going to go ahead and assume that your particular GM isn't the kind who would say you can't use a lump of wood or table leg as a club (which you are proficient with) because it's not exactly the kind of lumpy wood that a club is designated as being.
One thing is trying to argue that the cool rock you picked up should be treated as a double-bladed scimitar, it's entirely another to say "this whacking stick is a whacking stick".
Basically the only thing you'd directly get out of that is proficiency with using specifically your lute as a weapon, and as a dabbling musician I can only scream silently at such a decision.
EDIT: If you really want to drive home the "cheerleader" role, you could potentially take something like Martial Adept and pick up a superiority die. There's no stat bonus attached to the feat (and 20 CHA really is quite nice), but you get access to things like Commanding Strike or Maneuvering Strike, which would let you play fangirl to the Dragopal by giving them more things to do with their reaction (there's also Rally, but it's a piddling amount of temporary hitpoints and temp HP doesn't stack with any other source of temp HP, of which there are many). As far as bar room brawl applicability is concerned, most maneuvers require only a "weapon attack", which includes unarmed strikes and throwing rocks/mugs at people.
I've been mulling over this very solid advice, thank you! I'm not trying to optimize but there are some good ideas here regardless, particularly the Martial Adept options for chearleading.
However I've already got a lot of "Hey have a die" as a bard. I don't want to slow things down even more by having people perform actions during my turn. And OOC I've had a tendency to "direct" battles for a while, and that just doesn't fit my current character at all. I consider it personal growth that the orc player sleepily attacked someone I'd just Hideous Laughter'd, and I didn't even try to warn him. Just told the DM about the save-with-advantage, then assured the other player that it was totally fine XD
More mechanically, I've already got a lot of use for my bonus actions, and we seldom take short rests.
Grappling is awful and doesn't fit my character though, so I agree Tavern Brawler is dumb, oOoO. Gotta pick something else.
Crossbow Expert is SO badass, particularly the offhand shot into a melee opponent, but doesn't fit at all. Same with Moderately Armored, even if I got the DM to allow +1 CON instead of the book's +1 Str or Dex (Dex??). No, here are what I'm actually considering now:
Skulker: Probably completely stupid. Is a bard automatically revealed by playing a song? Probably. Unless the DM decides I'm echoing my music off the walls or something. I wouldn't bring it up except that I have double-proficiency in Stealth from when this character was an NPC.
Lucky: It's similar to what I already do as a bard, but MORE and stacks. This is a strong candidate.
Inspiring Leader: 7 temp HP for everyone is okay I guess, but I'm not a leader, and there's only three of us, this just seems weak.
Resilient (CON): I should stop obsessing about my odd CON probably. Proficiency on CON does sound pretty useful... Except we have a paladin to cure disease and poison.
Defensive Duelist: I like the idea of surviving melee, but this is probably a weak use of a feat
+2 CHA:
Let's face it I'm cute~ Almost certainly the best choice, and not even out of character at all.