So do you want a colour that would go with most things in your wardrobe? Navy? Black? Charcoal? Brown? What about a darker olive or forest green rather than khaki?
So, smart(er than what you already have) but not formal. Ideally showerproof. Not prone to creasing/attracting lint. Do you want it to wear now? As if you're looking at unlined linen jackets that would be very lightweight - not much heavier than a shirt, really?
I get hot very easily too, but at this time of year I would choose something lined/lightly quilted.
What size of bag do you want to carry it in? My everyday bag is a big soft leather tote, & even if I can't fold a jacket up inside completely, I will often fold it vertically & carry it on top of the bag between the handles.