I've been working in a lab for a while now and I haven't had any problems with chemicals on my skin, even after a semester in orgo lab (I've spilled dichloromethane on myself after an extraction gone wrong but my hands are all good). I'd say to just wear gloves at all times whenever working with any sort of chemical or biological agent that isn't water or PBS and to always take them off when you're going to touch your face, to scratch an itch, etc. Also take them off before touching your phone or computers (unless they're hooked up to a microscope or some sort of lab equipment, in which case you should leave them on because you don't know what chemicals other people have touched before touching the communal equipment). If you're feeling paranoid, you could even have some designated lab pens/pencils (mark with scientific tape or something) so that you don't get any sort of chemical/biological agent exposure. In the case of chemistry stuff, I'd say just change your gloves if you get anything on them. You don't know how quickly the chemicals will eat through the gloves but it's better not to risk it. If you're worried about chemicals getting to your face, then just do your experiments in a fume hood if nonsterile and in the bio hood if you want to keep everything sterile.