If you want to go the OEM route, the RCD510 is within your budget. Though you will need the Bluetooth kit to make use of the telephone and BT streaming features, if you're not fussed with that then you can just connect the USB/AUX cables and route it to the glovebox, armrest or near the ashtray (with the USB/AUX switch ports). Be aware that early versions of the MK5 GTI's will require a new Canbus Gateway to prevent the battery from draining with the new headunits.
There are some cheaper "copy" units out there available on eBay which seem to cram all kind of features (i.e. Android OS) but beware, they can be hit and miss in terms of usability and reliability.
For aftermarket units you have a wide choice, it depends on your preferences really. IMO I think headunits with built-in screens are better suited to the Golf cabin then the cheaper matrix units. Kenwood, JVC, Sony, Alpine and Pioneer makes some decent units in this sector so just have a browse of the features relative to your budget (also check for compatibility with iPhone 5!). Currently I'm rocking on a Pioneer AVH-2400BT unit for over a year now and it generally hadn't let me down. You will need to buy a Canbus Quadlock adapter and double din fascia kit if you go down this route.
