I can't say for sure, but I think that Brita filters exchange disolved solids for salts...
There was a huge debate about them on gw a long time ago, and I think the general consensus was they were not worth the risk.
No matter how you cut it, for a modest colleciton, a 50 cent gallon jug of Distilled water is the absolute cheapest way to go.
If you used tap, and your worried about it's effects, then hold your pot over a sink, and slowly pour a gallon of distilled water through the pot and let it drain. it's a waste of water in that you can't use it again, but it should help flush the media out.