How to seal porcelain so that the sink will be easier to clean?
If you've got the time, don't want to get rid of the piece, and have some degreaser and muriatic acid lying around, you might save a few bucks.

For any application of coating, preparation and the right materials are essential. After getting rid of caulk and taping off, filling in chips and cracks with epoxy, some light sanding, an acid wash and degreaser, you'll have a surface that's as ready as you can get. Try something along the lines of 2000 grit with a light touch to keep the surface nice and smooth. You're not looking to strip the current coating, but put a little tooth into it. Blow with your compressor (I always tape an airfilter to a cheap box fan to gather up the dust) and you're ready to go.

When the surface is clean and ready to go, don your PPE, ventilate, and give a few light applications in succession. Usually, you have to let the current coat get tacky before the next. Don't try to spray heavy, because you get runs that have to be cleaned. The technique for spraying is finding the appropriate distance, and doing smooth passes in a line in succession. Of course, follow whatever instructions the product gives you.

On such a small unit, I wouldn't buy any fancy kits. For less than $15 you can spring for an aerosol solution. Don't bother messing with rolling and brushing this stuff on. Be careful because there are spray products meant for appliances like washers and driers and it's cheaper in cost, but not the same.

In my way of thinking, if it's a nice piece, you work quickly but carefully, then worst comes to worst, you're out of an afternoon of time and maybe $20 worth of materials if you're not satisfied. Then you can go pick out a new one, and you have the experience to tackle the same project again down the road.