Here are my favorites for countertops rather than a comprehensive list. I have marble in the kitchen right now and while I like the look of it, I absolutely hate how high maintenance and prone to staining it is!

It’s expensive, needs to be sealed repeatedly and will show any stain and believe you me you’ll be making many! I can point out where my hubs made margaritas, where my youngest put down her popsicle and where I sliced tomatoes. Lot of people don’t mind the stains but I do. I never feel like it looks clean. However, in certain areas and price brackets it’s almost mandatory to use marble. People expect to see marble counters in kitchen in homes over a million around Farifield county, whereas granite is a norm in homes under a million. Honed marble will look more flat, doesn’t scratch but stains. Polished marble will be much shinier, but will etch and scratch lot quicker.
There’s been a massive growth in the variety of engineered stone and they are great. These quartz based counters all originate from the same source developed in the 60s by Breton company in Italy and are licensed by different companies (Caesarstone etc) and made look different. Engineered stone is super durable, doesn’t stain, and is heat resistant. You can get any look or color variation you desire. It is expensive but IMHO totally worth it. Typical costs range from $55 to $155 per square foot, installed.
Caesarstone

Silestone
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Cambria
Here’s an excellent article on which engineered stone looks most like marble, HERE.