What to wear over a t-shirt?

I've basically been following the basic bastard guide. Trying to put a little bit of effort into my clothing but I'm stuck on what to wear over a t-shirt. I live in Australia but general advice is appreciated.

For now, I've gone with:
Olive, tan and navy chinos
White/black/navy t-shirts
Brown boots/white sneakers

If I wanted to get two (total) coats/overshirts to suit this ensemble what should they be? What colours will work with everything I already have?

I've looked at some of the photos and I like the shirts that look simple and clean. I've attached some of the ones I like. Is there a name for this kind of thing?

And what about material? I travel a lot so something that doesn't wrinkle easily is a bonus.

Apologies for the dumb questions. I don't know what it is about clothing and colous. They just don't compute for me.
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