The sink fixture when installed never sealed properly and water can seep between the portion of the faucet that meets the sink basin. Just a small area - I'm not replacing the sink - just can't and won't. I had used some clear caulk around the base of the faucet fixture, but it came off after a few months: it was silicone, but in the fine print it says that it was for windows and doors (I just took the tube he handed me then left). It worked fine while it lasted, but what type would you suggest?
Whatever you use you have to get the sink up so you can fill the space under it. You can't just fill the crack because it won't seep in where it can get a grip.
the silicone should be sufficient. you may not have installed it properly. you have to make sure that the area you are sealing is clean of previous caulking. you also have to make sure that the area is very dry prior to putting the seal. then once you put the caulking on make sure you don't use the sink for 48hrs. Avoid getting it wet. It should last after that. you could also put some plumbing putty into the space then put the caulking. You might want to check under the sink if there is a way for you to tighten the faucet down to get rid of the gap.
