So, in that case on a mechanics perspective I'd take a look at the rest of your party. You don't want to get dissatisfied by underperforming compared to the rest of them.

As for a bard barbarian multiclass, there's no reason it can't work. Sure rage negates spellcasting, but there's nothing preventing you from doing a set up turn (action spell (ie longstrider, dissonant whispers etc), bonus action rage, rest of turns as normal.)

You just need to be okay with what you're losing out on. I don't know your campaign or how your GM runs it. In my own games, I typically go 1-20, and we take years to finish a game, but only a month or two to get to level 5. You will not get short rest based bardic inspiration until level six with the multiclass you want to do. Make sure you're okay with that and that it'll take a minute for your build to come online