Make sure you are not living in a state where collecting rainwater is illegal.
http://fellowshipofminds.wordpress.com/2010/08/01/its-illegal-to-collect-rainwater/
Last I checked they include Utah, Colorado and Washington but some will let you do it with a permit.
This first. Utah and some other south states have water "claims" where the first person upstream of where the water originates gets a quantity "stake" on water. Something like that, it's not that difficult a concept, but I forget what it is.
So, um, I did a master's project/"thesis" on global rainwater reuse and design.
Personally, I would not use rainwater for drinking. Having said that, note that it's fairly common in Australia to use raiwnater from the roof directly for drinking untreated, and LOTS of people worldwide drink groundwater from wells directly without treatment (I was a bit shocked when I learned this).
Bla bla bla, not legal advice, don't sue me. If you do want to go ahead, first check if you're allowed to by state. Then think about your collection system. There are lots of guides on helping you make one. Not a single state in the US of A (that I recall) legally allows people to collect rainwater for potable purposes. Most you can do is launder, wash shit, water garden, flush toilets, etc. (non-potable) - see Oregon, Texas, New Mexico, California, Colorado.
On the contamination front, you have to worry about your conveyance surface (i.e. roof and gutters). That shit can leach toxic shit (e.g. lead, mercury). Then there's the environment: your neighbour's chimney/meth lab dust, all the shit on the street and 50 blocks away blows onto your roof and sits there to be "washed" by rain. Then there's bacteria, but I'd be more afraid of heavy metals.
You could treat your rainwater, but you'd need something like micro-/ultrafiltration membranes, a UV system, and probably a chlorinator if you plan on storing your water for any "lengthy" period of time. Then you'd want to regularly test it at a certified lab to make sure it stays safe. Also, if any member of the "public" comes to drink your water and they get sick, they may be able to sue you, especially if your state has laws for rainwater: if they say you can't drink it, you fu*ked, and if they just don't say, well, then you're still fu*ked because it's neither legal or illegal.
Long story short, too much work. From a cost-benefit standpoint, toilets and landscaping accounts for a big chunk of your water use, so just take those savings and run with it.
Edit: A Brita filter is just a granular filter probably meant for taste and odour. I don't know much about it, but water treatment systems using sand filters use them just to remove the majority of finer sediment, and some bacteria. Viruses may be small enough to slip by. Don't even know how it works on dissolved stuff.