the new pi has built in wifi. i have the pi 2 with a wifi usb. you don't really need wifi for an arcade build, just ssh into the pi to download/upload as needed.
bought the cabinet from craigslist, it came with the x-arcade dual joystick and pi for $150. so def buy a used cabinet, also reused an old computer to save you money. the x-arcade joystick is selling online from $125-$150, that's if you want a pre-build joystick, otherwise you can buy buttons/joystick kit for less.
i got the marquee printed from a local sign shop. price for 24"x17" is $20-$30. i'm still working on the side art and bezel. i got a quote for one 136"x70" side art at $100/piece.
as you can see, it can get pretty expensive. not including time/labor. the hardest part is configuring the joystick. there are some great youtube vids for this step, but still requires a few hours of configuring.
i'm estimating the total cost would be $500-$700 to finish. you gain some appreciation for this kind of hobby and understand why arcade cabinets are sold for thousands of $$. it's a fun hobby, something i've always wanted to do.