Without knowing what kinds of gunk is in your water, that's hard to answer. Brita filters have a small micron filter for removing particulates as well as a carbon filter for removing some dissolved organic compounds, but they really don't remove all that much from your tap water.
When you say, "whole house water filter," what does that mean? Is it a reverse osmosis system, a steam distiller, a water softener (which you shouldn't be drinking from) or some other filter I haven't listed?
If it's a reverse osmosis or steam distiller, chances are you wouldn't need to filter your tap water any further. In fact, you may need to add back some potassium and magnesium salts back to it to make your water potable, much less brew-able. Highly effective filters like those remove almost everything from the water, which makes the pH highly unstable. Potassium, magnesium and calcium added back to the water can buffer the pH and keep it from swinging wildly from acidic to basic and back.
If I were you, i'd check with my local water company and ask to see a copy of their annual water analysis report (which they publish yearly). After reviewing it, compare it to the local water conditions for the styles of beer you're brewing and see how it measures up.
Worse comes to worse, add 50% tap to 50% filtered and see what you get. You might throw in a teaspoon of yeast nutrient as well if the water is very pure and low on total dissolved solids.
