Spax makes screws that work exceptionally well for this application if they're frameless cabinets. They're called rear panel screws, 1.25" length #8s, but the head and thread is made to work well in MDF/particle board. They also make some MDF-specific threaded screws in other sizes, but the wafer head on the rear panel ones makes a nice, clean finish with melamine.
If you have face frames, make sure you find something with no thread for a good part of the screw. It'll make it much harder to get a tight join and you'll be creating expansion/contraction issues down the line. Finish screws are not a good idea...you're relying on the strength of the head for your joint holding power, not the threads. Invest in a good countersink bit, predrill, and use ones with a nice bugle head. Or alternatively use a small forstner bit (slightly larger than the head size) and use washer head screws.
Also, regardless of how thick the joined materials are, you don't need more than 3-4 threads engaging, usually around 1/2". Never go more than 2/3 the thickness of the adjoining material for your embedment.
Source: architect, woodworker, former custom kitchen installer.