Contact cement is THE adhesive for attaching laminate to the substrate.
Follow the directions and watch out for the fumes if using solvent-based cement.
Pay attention to the part of the directions where it says something like "Once the two coated surface touch, they are pretty much permanently stuck together." Hence the 'trick' of laying a bunch of dowels or thin sticks on top of the adhesive-coated substrate and then carefully laying the adhesive coated laminate on top of that, and finally pulling out the sticks and then pushing the two coated surfaces together.
+1 on putting a solid-wood banding/edging.
But I believe the more durable way to attach the laminate and the edging in order to avoid the laminate going all the way to the final edge or having a lip/seam that can catch or start to peel, is to attach the laminate to the top first, then flush trim the laminate to the substrate edge, and THEN apply the solid wood banding/edging. Flush-trim the top of the solid wood to the top level of the laminate, and then apply the desired edge treatment (chamfer, round-over, Roman ogee, etc )to the solid wood.
Also keep in mind that if MDF gets wet, it will swell and warp and such. And although (usually) nicely flat-surfaced, MDF is darn heavy for its size and low strength for its size. Decent plywood is (usually) a bit stronger and more durable overall than MDF.
YMMV.