There are a lot of faucets out there. Three things narrow it down.
Where it mounts
Wall-mounted — comes out of the wall above the sink
Countertop — installed through the counter (you'll hear this called deck-mounted)
Sink-mounted — attached to the sink itself
Which one works depends on the size of your sink and how many holes it has — or needs.
How you control it
Handle style changes how you set hot and cold: lever, cross, double, knob, or touch-free.
Still not sure?
Most plumbing supply showrooms will walk you through the look-and-function side of it. That's what they're there for.
Stick with brands that have been around a while. They're built to be repaired, and they still make parts for fixtures they sold decades ago.
Delta · Brizo · Kraus · Moen · Kohler · American Standard · Grohe · Toto · Hansgrohe · Geberit
A $30 lavatory faucet from an online marketplace you've never heard of is a different story — there's unlikely to be a replacement cartridge for it in five or ten years. Fixtures like that are disposable by design: meant to be replaced, not repaired.
And your water matters as much as the fixture. Good materials buy you longevity. Good water is what keeps a faucet working the way it should, year after year.
An EPA labeling program. Products, homes and services carrying the label meet EPA standards for water efficiency and performance — you use less water and pay less on the bill. The label just makes them easy to spot on the shelf.