unsanded latex caulk. Sanded is used to match the look of sanded grout. You want simple color matched unsanded caulk. Buy yourself one of those $5 tools press hard and drag across. People tape off caulk but problem is when they pull tape up it pulls edge of caulk up also destroying the bond to the surface. Go to H Depot go to their tile isle and look by the grout. They will have a display with unsanded grout in several colors. Pick what is close and your done.

Btw i used paintable silicone last time. i wasnt painting it, just what i picked up do you think this wohld have contributed to the premature yellowing ? what reallt is the dif btwn paintable and non paintable

Caulk needs to be painted, and I'd recommend Big Stretch caulk. Hairline cracks fill best if you pull out the existing caulk, or cut out where the crack is first. And a picture or two of what you are fixing will get you the best responses.

This is 101 DIY. Even if you don't want to do it, you need to. Because the substrate under the Formica is probably particle board. A leaking sink rim & particle board should not be allowed to wait for 2 months to get repaired. The particle board is getting wet & when it gets wet, it swells and crumbles. I'm not a youngster by any means & installed my sink and faucet. The only thing that I needed help with was removing the old cast iron sink. You need to shut off the water, disconnect the faucet hose at the water source & disconnect the drain. Lift the sink with faucet still attached out of the hole. ( I primed & painted the raw particle board edge & underneath for a little extra protection in case of leaks.) Since your faucet has goop around the base, that indicates that the faucet wasn't installed properly. It may be that it just needs for the fasteners to be tightened up. Or it could mean that the bozo installers left out a piece that goes under the faucet escutcheon plate (depends on the faucet--may not have one.) I used plumbers putty as outlined above on the underside of the sink rim. Because I wanted the sink to be easily removable. (Plan to relocate the sink later.) With the faucet firmly affixed to sink & the rope of putty on the sink rim, set the sink back in the hole. Attach the clips and tighten until the sink is firmly set (no gaps) on the counter. Reattach the water & drain lines. Check for leaks at those connections. I use a Kleenex to check for leaks. A tissue will let you know if there is even the tiniest seep at connections. I didn't have enough room in the cabinet to install the clips on the sink ends. I could have cut away some of the cabinet sides to make room for the clips but it would have been very difficult to position them. So, I omitted them. Not the ideal but the sink doesn't leak. Putty plus clips on front & back sides have been sufficient.