Serious chefs travel with a packet of their personal knives, but the all-purpose knife is the Chef's Knife, aka Cook's Knife. My chef friend only uses Gunter Wilhelm knives, but chefs are cooking all day.
I guess the high-carbon, high-maintenance ones are the best, but whatever. I like the ones with a curved blade so you can rock it when chopping garlic, parsley, etc. Maybe you only need two knives: a bread knife and a chef's knife.
You can sometimes find used high-carbon chef's knives on eBay.