Disclaimer
I've tried to make sure what's in this answer is accurate. However, when doing any work that can affect your own safety, always carry out your own risk assessment and consult a professional about what protective equipment you need. This is not professional advice.
You're looking at three major types of respiratory protection (well, 4 if you really go down the serious end). They're illustrated nicely by this page.
Dust masks
These are basically large-particulate filters. They're good at filtering out dust, sawdust and chippings, but you should never use these for chemical work - the filter just won't catch them.
Fine-filter half-masks
These vary much more. They're essentially the modern-day equivalent of a gas attack-mask. If you're buying one of these, talk to the store personnel about what protection it offers - some are large-particulate filter-based, others are fine-filter-based and will filter out smaller stuff, even down to chemicals.
Powered respirators
These actively filter what's in the air to remove harmful substances. Again, the quality varies, as does the battery life.
And finally, for if you're doing really dangerous work (such as work with airborne toxins) or you're paranoid about breathing chemicals, you can get a full oxygen system such as that used by firefighters or divers. That has the advantage that if the mask is intact, you get ~100% filtering; it has the disadvantage of being clumsy, heavy, and difficult to fit correctly.
Whatever equipment you get, make sure you get it from a competent reputable supplier, such as 3M.
And finally, when doing work with chemicals, you need to look for eye protection too - many of the chemicals that can damage your respiratory system can also damage your eyes.
