Advice?
Build a sawboard for making straight cuts; see the sticky at the top of the forum.
Buy, borrow, or rent a circular saw for making straight cuts. You can use a jig saw, but you'll get better results from a circular saw. Feel free to buy a used one from Craig's List or eBay, then put a high-quality blade on it.
Don't use MDF. Use MDO (medium-density overlay) or plywood instead. The Project Arcade cabinet is drastically overbuilt and will weigh, quite literally, a ton if you use MDF.
Use Titebond wood glue in addition to screws for your fastening.
Buy a 12-inch combination square and use it. If you can afford it, buy a Starrett. The cheap ones are a pain-in-the-butt to move/adjust, not terribly accurate, and difficult to read. I've used my Starrett combo square on every wood, metal, and machining project I've done since I got it. I don't regret the expense and I'd buy another one in a heartbeat...