Question:
I want to get a water filter system that will filter my drinking water at the tap and also filter the water going into my refrigerator. Can someone recommend a type and brand?

Answer: I have an Omni under-the-sink filter for the kitchen tap. It has 2 stage filters. I notice a big difference in taste and clarity with it. Plus, I have small kids and lead solder, so it hopefully helps there. Although just running the tap for a minute or two probably clears the lead. You can buy different filters in different combinations for whatever problem you're trying to address. Some can filter asbestos and MTBE. Reverse osmosis systems are supposedly the best, but they're more expensive and require a tank under the cabinet.

I also purchased a GE brand in-line filter for the icemaker in my fridge. You just splice it into the copper line.

You can get a whole-house system, but in my case it would be filtering before the lead solder. And I see no point in washing clothes, cars, dishes, in filtered water.

I installed the Everpure ROM II about 8-9 years ago. It has two cartridges, one of which is Reverse Osmosis (RO) and the other is a prefilter. The prefilter removes chlorine and dirt kinds of things, both of which would harm the RO cartridge. The RO removes dissolved solids. The system produces excellent drinking water. And, not wanting anything less in iced drinks, I ran a line up through the wall, through the atttic, and down to the refrigerator ice maker. There is a bit of sticker shock with this system, but IMHO you will find none better. The cartridges are also expensive, but they need to be replaced very seldom, at least in our area. As I recall, I've replaced the RO cartridge twich since installing it, the first time probably unnecessarily since I had not yet bought the dissolved solids tester to see when it's needed.