I haven't been able to find a definitive statement of "Kellids favor these weapons", but there are a number of elements in the lore that give clues.
Types of Kellids
The Pathfinder Wiki describes "Kellid" as a blanket term that covers several groups:
Isgeri: The predominant Kellid ethnic group of southern Avistan before the coming of the Azlanti successor states. The Isgeri were largely absorbed by the Taldans and Chelaxians of Druma and Isger, but still hold onto their traditional cultural practices.
Palakari: A unique blend of Kellid and Taldan heritage who make up the majority of humans in Druma. Palakari are the least stereotypically "barbaric" Kellids, and many identify more as Taldan depending on their upbringing.
Sarkorians: The proud survivors of old Sarkoris, now in diaspora throughout central Avistan. Most Kellids in Numeria, Mendev, Ustalav, and the Worldwound are Sarkorians.
Yurktiri: The embodiment of Kellid culture to ignorant outsiders, Yurktiri are the people for whom the Realm of the Mammoth Lords is named.
Since Iron Gods takes place in Numeria, it seems likely that your character would be a Sarkorian.
Official artwork often depicts Kellids with large metal weapons such as greatswords, longswords, two-handed hammers, and in the case of the iconic barbarian Amiri, a bastard sword made for a frost giant.
While Kellids are typically thought of as barbarians, they did have their own kingdom at one point - Sarkoris. Before it was destroyed by demons when the Worldwound opened, it had some significant cities and mines, as well as skilled stone and metalworkers. This helps to explain the prevalence of metal weaponry in their societies. As a Sarkorian, your character would likely have access to weaponry made during that time, even if your tribe no longer has cities or mines of their own.
According to the Inner Sea World Guide, Kellids frequently worship Gorum, whose favored weapon is the greatsword. Other popular faiths for them are Desna (starknife), Erastil (longbow), and in some places Rovagug (greataxe) and Minderhal (warhammer).
The Pathfinder Wiki also indicates that many Kellids follow the Green Faith. This could incline them towards druidic weapons like spears, scythes, and quarterstaves.
The Kingmaker adventure path features some Kellid NPCs. They're said to come from the Realm of the Mammoth Lords, which would make them Yurktiri. They are depicted wielding battle axes, greatswords, greataxes, spears, and throwing axes.