Some things to know:
As of Jan 1, 1996, two major things changed with respect to the circuits you're working on. First, the "appliance branch circuit" (the circuit from your service panel that supplies the kitchen countertop outlets) had to be GFCI-protected in new construction and renovations, and second, that same circuit could not feed the disposer or dishwasher.
The upshot is that how you deal with this depends on how your kitchen is currently wired, which depends on the build date and/or the date of last renovation. If your home was built or the kitchen last redone after 1996, the dishwasher and disposer should have their own dedicated circuit (your wiring is illegal otherwise). That makes it very simple; swap the under-sink outlet for a GFCI. A GFCI breaker is available, but the outlet type are better IMO (They're closer to the source of the fault so they trip slightly faster, they're right there to reset should a fault occur, and they don't require you to shut off your entire house to install and replace them). The downside is that you'd have to have two outlets under-sink.
If the same circuit that supplies the disposer and dishwasher also powers the countertop outlets (common in pre-'96 construction), then more than likely, the GFCI should go on one of the countertop outlets, and you should replace the under-sink outlet with a normal outlet. Specifically, the GFCI should go on whatever outlet is the furthest "upstream" on the circuit (the one that receives power directly from the panel breaker, or is the closest to that one that you wish to protect), which is usually very unlikely to be the J-box under the sink. GFCIs can only protect the portion of the circuit that is "downstream" of the GFCI; they cannot kill power to anything "upstream" in the event of a fault. This was a little tricky in my house, where I found that I have two appliance branch circuits in my kitchen, one of which powers the fridge, microwave, and one outlet, and the other powers the dishwasher, disposer, and three appliance outlets. I wanted to protect the outlets and disposer/DW, but not kill power to my fridge if something should trip while we were out of the house. I found a way to make it all work for me, but your experience may vary.