You wanna stay away from deodorant that contains aluminum. I recommend Tom's (available at Target). Haven't had a problem with pit stains since.
I work in the inland empire and it gets super hot there. I usually wear a light v-neck undershirt, as lighter color shirts can be see through and if you're not wearing a jacket, it might be something to consider … BB's undershirts are good. When it's hot, I'll wear a BB linen button down or the Brookscool OCBD.
I hope this helps!
The problem with Tom's is it doesn't work well for some people. I've been using Kiehl's, which has aluminum, but is a cream so you can use a small amount. Every third or fourth wash, I'll make a paste with oxyclean and scrub the pits and the collar with a soft bristled brush. If you can allow them to soak a bit afterwards, even better. Removes 95% of the stains. This is coming from someone who does not wear undershirts.