Go to your local hardware store and pick out some 3/4 plywood. If you’re going to paint it you can get “paint grade” which is relatively cheap. If you’re going to stain it, you probably only need one good side. Pick a wood you like, and ask them to cut it in half for you. Ask if they have any half sheets of anything, too. You’ll only need about 1/2 a sheet. Most stores with plywood have a panel saw on which they can cut sheets in to manageable pieces for you. (If you can transport and carry around a full sheet, you still may want to cut the sheet in to smaller pieces by hand before wrestling with it on the tablesaw.)
Cut two pieces 48" x 12". Then rip two and a 1/2 inches off of each piece’s width, and glue and screw it back on at a 90 degree angle to that same edge (predrill for the screws so that they don’t split the plywood). This will help keep the ply from sagging under use. This is the front edge upon which your elbows will rest, so you may want to sand or ease this edge a bit.
What you have now is a pretty strong shelf that should hold your dinner and books just fine. But you need to hold up the shelf. It’s nearly impossible to have it unsupported over a 96" span, regardless of how it’s attached in the middle. It’s actually not really recommended that it be unsupported over a 48" span, either, but that’s a judgement call.
I’d advise a permanent cleat screwed in to the side of each bookcase that the shelf can be set on, and removed. You can use a piece of 3/4 ply 8" x 2" for each. Place the top edge about 29 and 1/4 up fom the floor for a “normal” table height. You can put it higher or lower depening on your chair.
Now, you need something in the center. I’d go with a third cleat on the wall halfway between the two bookcases, and a leg in the front. That way the shelf is supported on both sides, as well as each end. Make your leg about 3 or 4" wide in order to support both shelves, and the same length (29 1/4?) as your cleats are from the ground. The more supports you put between the bookcases the better. Three legs would be better than one. Cleats on the back wall between the bookcases would be better, too.
All the points where the shelf meets the cleats and the leg should be screwed rather than just setting the shelf on top, but that’s up to you. It’ll be noticably wobbly without screwing it together. Fine for eating pizza and reading comics, not so good for soup and Shakespeare.
Not to sound like your mother or anything, but please, for the love of Pete be careful with power tools which are new to you. It’s very easy to lose an appendage on a tablesaw, or lose a testicle from kickback.