If you get a USB/AVR-duino like the Micro here on the Arduino site then writing HID becomes Easy and your serial speed hits USB 1.1.
Notice the Micro has pins perfect for inserting into breadboards or pushing female DuPont cable ends onto.
It's 40 wires, not 40 cables. That's $1.25 for one 20 cm (8 in) 40-wire cable, pretty cheap! Get 2!
You peel off as many wires as you need to make a cable (serial uses 3 minimum) then split off ends as needed to reach all pins. The result is never perfect but far cleaner than a rat nest of jumpers.
Those USB/AVR chips are all surface mount, not the simple DIP (Dual Inline Pins) that can plug into a breadboard.
For a control stick you can get excellent results pretty quickly with any USB/AVR or USB/ARM board.
When I learned it was on a Teensy 2.0, the Leonardo hadn't been made yet, PJRC has tutorials and made a lot of code public so I lean toward them for making it easy and having good prices.
You can use almost any Arduino to program most AVR chips made, from 8 pin ATtiny45 on up to the 40-pin "Mighty 1284". If your design grows, there might be a bigger AVR to migrate to, the code will be the same but the pins may change and almost like magic your project will have more space.
If all you want is moar pinz then learn about daisy-chaining shift registers on SPI bus, people run 100's of leds to make displays with Uno's and show it on Youtube. The wild ones spin around to make POV displays.
If you want storage then look into SD modules, you can buy them cheap or make your own cheaper.
The UNO with the DIP chip in the socket is designed to develop a program on the chip. You then pry the chip out and put it in your end product, pull another bootloaded 328P from your stock and work on the next thing. The board is a dev board, not an end product component. That should be smaller just to start. Much smaller, like a Micro.