Welcome to the hobby and welcome to the community!
1. I've just finished by first cabinet (look out for my first "Projects Announcement" post soon) and I went with plywood for my build. I've had no problems with the material but I think the next cab I build I might go MDF. the weight and breathing hazard of working with MDF sounds like decent trade off compared to some of the issues I've had using plywood. MDF is seamlessly and consistently smooth and well constructed for a cheaper price. I paid a little more then $30 a sheet for BC grade plywood. When it was time to paint, I had to carefully and aggressively sand it for a velvety smooth finish, one of my sheets wasn't even 100% square on one side, right now I'm in the painting process and I see this thing is gonna need a few coats to really get that consistent professional finish (the grain of the ply wood faintly bleeds over in some areas on the first coat) and don't even get me started on the warping. Right out the damn store a couple of my sheets were slightly warped. I had to cut a few panels over and really get creative with the assembly so that it all fastened together nice and straight, it did in the end, but I feel like I wouldn't have had some of these issues AND saved money if I went with MDF. Plywood isn't bad at all. My cab looks nice so far and so will yours, but take precautions. Check your sheets for squareness and little to no warping at the store. When you get it home, still be aware of warping, I heard even letting the sheets sitting around to long can cause them to warp overtime because of humidity. Sand your cab down silky smooth before painting and give it a nice couple coats of prime. So from my personal experience, you can have a great cab from plywood, but next time I think MDF might be easier for our use.
2. Consider yourself lucky, I spend a fortune on all my tools before I even bought any lumber. I had NO decent woodworking tools so I had to build up my tool shed from scratch. My Jig saw was I think $80, the router was about $180, my worm drive circ saw was also about $180. And I bought all kinds of measuring and layout tools and other little stuff like a sanding block, sand paper, all kinds of squares, screws, bolts, router bits, forstner bit, spade bits. I don't even wanna look back on all I spent from the start, but it's okay because the progress makes it all worth it! So trust me mane, $150 is good money compared to a city boy like me with no tools to even start.
3. I think a 23" CP can fit a 2 player street fighter style setup just fine. Now if you want to throw in a trackball, spinner, dedicated 4 way stick, dual stick setup, and other controls you may want to reconsider. I say less is more. A simple, clean panel that can play most games is better then a sloppy, ---fouled up beyond all recognition--- up panel that can play them all. Keep in mind you and your partner will be rubbin shoulders while playing, which I personally like anyway, it reminds me of the experience of being in an arcade, but I know some people prefer a big spacey 4 foot panel that's independent of the rest of the cab.
4. Are you mounting it vertically or horizontally? Either way 17-19" sounds like the sweet spot for a 23" panel. Either one will fit nice, it's just a matter of price and availability, but I wouldn't go no bigger or smaller then that.
5. All that sounds just right for a simple 6 button 2 player setup. Hacking a PC game pad is something I don't see often though, most people go with a $40-$50 keyboard encoder from GGG or Ultimarc. As long as you familiar with the pad and know exactly where to solder, you should be fine. Only thing is, will you be using the pad hack to also wire your coin door?
6. I ain't mad at ya, you don't know how bad I wish I can order my coin door today. I'd probably tinker with the damn thing and play with it like a little kid before even bolting it in lol.
My advice, keep it clean, keep it simple, and plan ahead. Most people have their own direction and vision with their custom cabs, especially in regard to controls. It's easy to get carried away and cover a little too much ground for one machine, but in my opinion the people that avoid the "frankenpanel" and keep it nice and simple always make the best cabs and I hope mines comes out just as nice. It's up to you how you want to make it, but in my opinion, again, less is more.
Also, if you haven't started yet, I suggest you consider Gozer's very accurate Google Sketchup model of those classic Bally-Midway/Namco cabs. Sketchup is a great software for planning and previewing out a cab build, it has a HUGE growing library of arcade cabinet models, and I think you'll find it very helpful for when you need an idea on how something will fit or look before messing with your actual material.
Besides that, BYOAC's own Javeryh built one of the most convincing Bally-Midway/Namco cab replicas I've ever seen, Bella's Arcade, and he kept a nice journal of his build. Check it out if you need any inspiration from someone who's done it successfully:
http://bellasarcade.blogspot.com/Good luck!