I've got pretty sensitive skin and anti-persperant caused it to crack and even bleed. So I tried the rock salt/crystal kind of deodorant. My local supermarket carries it, should I ever run out, but I've had the same one for seven or eight years now. It works pretty well for me.
I also shave my underarms, which probably helps -- less surface area for bacteria to grow and sweat dries faster. If I'm wearing a tight shirt, I'll sometimes use baby powder in case I sweat, but in general it hasn't been a problem.
I bike to work occasionally, but usually change my shirt and wipe the sweat off with an alcohol wet-wipe. That helps as well.
Also, natural fibers are your friend! I will get stinky if I wear a polyester or rayon shirt all day, but that happens even if I wear normal deodorant.
"I also shave my underarms, which probably helps". Interestingly, the Wikipedia article on this topic claims "Underarm hair wicks the moisture away from the skin and aids in keeping the skin dry enough to prevent or diminish bacterial colonization. The hair is less susceptible to bacterial growth and therefore is ideal for preventing the bacterial odor."
Have you tried a mild skin antiseptic cream? I've used Savlon for this in the past (cetrimide & chlorhexidine gluconate are the active ingredients, in a white vanishing cream base). Doesn't block pores, but is effective at killing most of the bacteria and is soothing if you have aggravated the skin there somehow.
I also shave my underarms, which probably helps -- less surface area for bacteria to grow and sweat dries faster. If I'm wearing a tight shirt, I'll sometimes use baby powder in case I sweat, but in general it hasn't been a problem.
I bike to work occasionally, but usually change my shirt and wipe the sweat off with an alcohol wet-wipe. That helps as well.
Also, natural fibers are your friend! I will get stinky if I wear a polyester or rayon shirt all day, but that happens even if I wear normal deodorant.