Fire > Thunder > Water. For Dragon, you can use True Shadowbringer.

The main things to consider when deciding which element you want to prioritize for your Gogma GS are elemental matchups and the craftable alternatives. A Gogma GS with a wide array of matchups and poor options for craftable alternatives, should logically be prioritized before one with fewer matchups and better craftable alternatives.

Elemental Matchups

Chart from Wilds Greatsword Guide by Jackscin and OPGZ2:

Fire has almost twice as many matchups as any other element, including standouts Jin Dahaad, Gore Magala and Lagiacrus. It’s used in some parts of the Gogmazios fight, too. Thunder comes in as runner-up with Seregios, Uth Duna, Omega Planetes and Mizutsune. Ice is pretty marginal with only four matchups, and even some of those are also weak to Water.

Craftable Alternatives

Dragon has easily the best craftable option in True Shadowbringer. With an optimal set, this GS comes very close to Gogma Artian performance in Dragon matchups thanks to the self-damaging ability Darkside, which translates into very high Resentment uptime, as well as a high amount of Dragon element. TU4 made the TSB playstyle even stronger by buffing the Nu Udra set bonus skill, Bad Blood, which creates extra damage procs while Resentment is active. Creating a Dragon Gogma GS that outperforms the TSB set requires a perfectly-rolled GS as well as a good RNG talisman, so it’s quite a heavy investment for a relatively small improvement.

Thunder has a pretty good craftable option too; the Lagiacrus GS High Lagia Blade. It comes with Focus, decent slots, and the Convert Thunder Resistance ability which gives a lot of element damage when you max out your Thunder Res to 40. It’s definitely no True Shadowbringer though, and will probably lose to that set, even on Thunder matchups. To be honest, the best use for the High Lagia Blade is probably to use it against Thunder-weak Omega Planetes, so you can get True Shadowbringer and stop using High Lagia Blade.

Fire, Water and Ice have underwhelming craftable options.