I say, "Go with melamine." It will be less work for you and probably a bit cheaper, too, by the time you fgure in the cost of laminate. You'll have to finish both the inside & outside for a decent looking cage made of MDF.
With melamine you'll already have both the inside & outside of the cage finished, just silicone (Silicone II) the inside seams, iron on the edge banding and you're done.
As for melamine chipping, tape both sides of where you're going to make your cuts, use a new saw blade (I use a 60-tooth blade) and don't rush the cut. No problems.
If you're not very handy you should be able to take your sheets to a cabinet shop & get them to make your cuts for you.
If you wanted a natural wood look I'd go with plywood and water-based poly.
Have a good one!
HH
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Due to political correctness run amuck,
this ol' hillbilly is now referred to as an:
Appalachian American