I have brick behind my range, the kitchen remodel has been in for about a year now. It was a chimney original to the house that I wanted to keep. We had it sealed with several coats of sealer that did not change the appearance of the brick. I wrestled with whether to leave the brick, paint it, or somehow cover it. While I liked the look of brick, I was concerned about the maintenance. When I found people that actually had sealed brick, they all seemed to think it was fine. Add me to the list. It's fine. It cleans fine. It's not filthy, greasy, etc (with adequate ventilation at least). We aren't a 3 meals daily from scratch sort of family, but the kitchen is used regularly and isn't just for looks.

That said, I wouldn't use real brick as a backsplash by choice. I did look at the home depot faux brick you have linked above and found it to be fairly convincing. I'm thinking about doing a wall of it when we finish our basement (there is actually exposed brick there currently unfinished, but its not realistic to keep as is). There are other good brick look tiles out there as well. Getting samples should be easy.

As for the countertop, you need something relatively simple or solid. I think everything the designer suggested seems too busy. Additionally, would probably not do a different pattern layout over the range, the brick itself is enough pattern. We used LG Muse which is white with modest amounts of veining. A grey could also work if you don't want the white on white look. Perhaps you've done this already, but try google image search "brick backsplash kitchen" and see what you like.