At the very least I would use a ledger block/dado system, especially if you're using MDF.
If you're not sure how to do this, hit Home Depot and get a "how-to" for building cabinets.
I personally opted for a frame and plywood on mine; but, then again, my brother-in-law and I built his daughter's first "baby-bed" out of 4x4's (w/ carriage bolts) and 3/4" plywood, so I'd say I tend toward overkill.
On the other hand, I have NEVER had anything I built fall apart.
That baby bed was just big enough to hold the crib mattress after she was old enough for a bed.
We BOTH jumped on it at the same time to make sure it would hold her.

Fortunately we didn't have to BREAK the bed apart when she was done with it.
At least we planned ahead for THAT.
Alot of the reason that I opted to frame mine was that I didn't know ahead of time what the final shape would be due to hardware issues.
I built a rolling table to hold the CP/Monitor, and then used cardboard to tweak the shape/size until I had what I wanted.
Once I had the right shape/size, I then cut the plywood to replace the cardboard.