Alright, I'm going to weigh in here - get ready.
Yotsuya and PL1 are on the right track. Evilnuff's going towards general WW rather than cab building. Absolutely no need for a jointer or planer for cab building, you're going to be using finished stock from the lumberyard. Also, for the cab sides you're going to need a circular saw, so skip the table saw. The small table saws you can get for cheap are too small to help with the large pieces on a cab. Plus, as Evilnuff has proved, table saws are super dangerous!

Same reason - jigsaw trumps bandsaw for this application and it's way cheaper. you need to bring a small saw to big work rather than big work to a bandsaw.
Pipe clamps - these are nice and I use them sometimes. However, most arcade projects can easily be clamped by drywall screws while the glue dries.
Miter box- for shortening long narrow stock. If you're just making 2x2 blocking for corners, you can cut those with another saw you already have.
same with handplanes - not for this type of construction because everything is painted or wrapped. If you're doing a woody - maybe.
dust collection - not for one project. use your SO or parent's vacuum cleaner and throw away the bag afterwards.
Here's my answer - you can build a quality stand up cab with the following power tools from Sears on sale:
-Drill - absolutely essential - get a small drill index and a small set of spade bits - consider a corded drill. they're more powerful and reliable than cordless and a much better deal. Cordless is great but doesn't help much on a stationary project. better for around the house/at the jobsite stuff.
-Jigsaw - if you have any curved cuts at all a jigsaw is essential. stay away from the cheaper one's here- they don't hold the blade at 90 degrees to the baseplate very well. they start to be OK around $60 or so. get good quality blades (i.e. bosch) and use them on materials as the package recommends - there are different types.
-Circular saw - for your straight cuts a circular saw is essential. Using a simple guide, you can reliably and precisely cut out your cabinet parts. The cheapest circular saw is pretty good these days for light work.
-Router - I would try to find someone to borrow one from. A $50 router or a palm router is ok for cabs because you're just swinging small bits. Don't get a laminate trimmer if it's your only router - too small for t molding bits.
That's it, the minimum I would go into a cab build with. I'd allow $200 for this stuff. I'd figure another $150 for small tools, t molding router bit, tape measure, sandpaper, good paintbrush, square, dust mask/safety glasses, etc.
good luck.