Luka straight up becomes mandatory by the beginning of the third route of part 3 due to being the only party member that consistently stays with you bc no matter the route and certain dungeons splits you up in teams of three where Luka illias and alice are mandatory party leaders of each team, you will inevitably reach a certain point you are separated from route exclusive characters while the third route does not discriminate and takes away story characters alongside the pocket castle (though the pc is temporary) and depending on the character it might be awhile before you get them back. So never neglect Luka or you will pay for it (I learned that the hard way). The same goes for Alice and Illias but to a lesser extent.
Otherwise it would be in your best interest looking into a dancer/singer for support. Singers and Dancers in generally are goated thanks to the buffs and debuffs at their disposal. Then you have the races with dancing and singing baked into their progression (Dolls, fairies, Sea-dwellers, Harpies, Lamia, and Kitsune) have their fair share of skills that enable extremely degenerate strategies. I personally would look into a Kitsune as in general have decent singing skills making them the best fit for that role. Something you'll notice is that the more you start investing into abilities, MP and SP costs can easily balloon out of control if you're not paying attention and that is before traits that further increases the costs of skills. Later levels gives Kitsune dancers the ability to lower costs before outright negating costs altogether allowing you to go all out with little risk.
I used Daji as my main support due to her signature weapon giving her 3 turns thanks to the power of shuffling party members. Her trait allows access to all job skills on top of a decent selection of races made available from the start which allows you to still use those skills even when you change her job. making her a frail but an extremely versatile support and thanks to a decent bit of races unlocked already, you can add more races on top of that thanks to promestein. And thanks to the Kitsune race you can get skills that mitigates before negating her main drawback of additional sp costs.
Since her weapon gives you a chance of getting either 2 or 3 actions per turn you can always get 3 turns all the time by going to shuffle party members and exiting out re-rolling her chance. couple that with chain skills which slowly start becoming more and more available, and she can easily top off your team in 1 turn. yeah the weapon slot cost sucks on top of a bit more investment in other areas, but she's definitely worth it.