I use a ZeroWater filter to get down to 0 Total Dissolved Solids and then third wave packets to reintroduce good minerals for coffee. Its still the case for me that this is cheaper than trying to buy distilled water or using distillation. Reverse osmosis is probably cheaper overall but a lot more initial outlay and it depends on how much water you need.
Brita and other similar small filters do a poor job of removing total dissolved solids (for me its the difference between 260 and 245 which is almost none removed) so they don't change the situation for coffee extraction all that much