first, yes get some 220 grit sand paper and sand it down again to get off any grime. ALWAYS sand in the direction of the grain. Never go sideways, it shows up in the staining process.
Now, get a quart or more of sand sealer. Sand sealer makes the staining especially on pine more uniform and keeps from dark and light spots. After applying the sand sealer, the wood will rough up again. you will need to lightly sand again. The moisture in the sealer makes the wood proud and expand outward. Sand it and then get a tack rag and get the dust off.
Now get a good stain like Minwax and use a rag to apply it. Do not use the brush way. Do not use the two in one stain where the polyurethane is mixed in with the stain. apply the stain in the same direction of the grain and do not over apply. put on one coat, and then decide if you like that or want to go darker or richer. The more coats the darker or richer the project becomes. APPLY THE STAIN IN A UNIFORM MANNER ALL OVER.
Now, when the look has been obtained with the stain stop and now consider the finish coat.
I would use a good polyurethane finish. decide on your sheen. I love satin because it has a low shine level and does not look plastic.
There are two types of polyurethane, oil and water. Each has their advantages and disadvantages. Oil will change the color of the stain and create a yellowing look. I do not like this look. water will not leave a yellow finish. Oil takes a day or more to dry, water takes 20 minutes. Oil collects dust, a real killer, water does not as much because of its fast drying.
I would apply five or six coats of water based polyurethane.
You will have fun.
Remember, when looking at stain examples. the same stain will look different on oak as it does on pine. so, do not make your stain color decision with out putting it on pine or whatever your sink is made of. If you look at Golden Oak stain on oak and you like that allot and your sink is pine, the color will not be anywhere near the color as it was on oak sample.