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 -- 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.