A few questions from a beginner

[Robert Vermaat]

Hi Matt, welcome to the ranks of the Late Roman army!

-- Pannonian cap. I handmade one myself for another project last year, but it's made of red wool. Does the color red signify authority/higher rank? I was thinking of making a brown one if red was reserved for officers and the like.

The colour does not signify any rank that we know of. Perhaps purple excepted.

-- Tunic. I have my tunic cut out and ready to be sewn up, but I have been waiting to apply the clavi first. Would lower-status troops have highly decorated tunics or would they be unadorned? I know plain clavi/orbiculi are now seen as a sign of a inexperienced/inaccurate reenactor, but would a poor-man tunic ever just have, say, plain clavi and nothing else? Also, are orbiculi or segmentae more accurate for 380-400 AD?

Decorated tunics signify wealth, and a common soldier would not be so rich to be able to afford that. besides, it's not something you'd wear into battle, with the chance to damage it.
Monochrome decorations can easily be 'enhanced', so it's no shame to start with those. I'd satert with segmentae, they are the easiest to fluff up.

-- Brooch. I have read that the crossbow brooch is tied to authority as a symbol of rank, especially gold ones. Would an old tarnished bronze one still be considered too "high-up" for a common soldier?

Bronze is just fine. Silvered and gilded brooches are for the officers.

-- Spatha baldric. For this 20-year time period, is the thin baldric more accurate? I have seen highly decorated thick ones with metal openwork pieces and phalerae, but was there any decoration commonly seen on the thin ones aside from a buckle?

A thin baldric would be best for the later 4th c. Wider baldrics are better for the 3rd c.