Archetypical gnomes

[Braininthejar]

There is a chance my party will antagonize a bunch of local city gnomes, and I'm preparing an encounter.

What classes would well showcase their style?

I was thinking an illusion wizard, a gunslinger and a bomb alchemist, but I need at least one more

[Mysterious Stranger]

Bard would be my choice. Gnomes make incredible bards. They are more suited for bard than wizard. Summoner would be another class to consider. Personally, I would drop the wizard and go with summoner and bard. Bards get lots of illusion spells so can handle the illusionist concept.

[Oli Ironbar]

If you find gnome only feats there are so many good directions. Bewildering Koan for gnome Monks, Tantrum for gnome intimidators, and a rage ability that’s just out of memory at the moment.

Pretty much any class as long as you do it in a new and curious way.

[Ju-Mo.]

You also could make it a sorcerer instead of a wizard.

There is no really good bloodline for illusion spells, but the Rakshasa Bloodline makes it harder to recognize which spells you cast.
Which can be good if you use a lot of Illusion spells.

Otherwise, Fey bloodline is thematically nice for gnomes imo, and it gives a +2 to your save-DC against compulsion spells. Which can be really nasty.