Trying to find a touchscreen that will be compatible with a microcontroller
Square touchscreen displays are not common; search for 4.3" touchscreens to obtain approximately the same screen area, typically in a rectangular 4:3 or widescreen format.

If you are not experienced in microcontroller programming, a serial touchscreen (SPI or I2C connection) would be easier to use than one designed for parallel data. 

Also, touchscreen and LCD display panels often communicate via a flexible plastic connector, which is not trivial to connect up if you are not experienced at soldering small pitch connectors. 

More suitable to your purposes would thus be a serial touchscreen module that comes pre-fitted on a PCB with standard 0.1" pin-out connectors. For instance, the $38 iTead ITDB02-4.3, a 4.3" color LCD plus touchscreen, which also contains an SD card socket that might find use in your project. (This is not a recommendation, merely an example product)

Arduino programming support for this module is available through the UTFT Library, saving some effort in just getting the device to work. The same library also works with a variety of other touchscreen and LCD devices, so changing to a different device in the future is an option.

For even simpler connectivity, look for an Arduino compatible touchscreen shield. These shields just plug right onto the Arduino board, so no fiddling about with jumpers or getting things wrong. Of course, there is a price premium for the convenience: EUR95 for this example. Cheaper ones do exist, with varying levels of library support and performance.

If you look at smaller touchscreens, or go with monochrome, the price drops significantly. There are often monochrome serial touchscreen modules on eBay for really low prices. Watch out for the connector the device uses, though. FPC would require that additional step of soldering up a very small pitch connector, typically 0.8 mm pitch with up to a dozen traces to be soldered.

Sites like Adafruit and SparkFun may also be worth a browse, not the least because they cater to the hobbyist community, so devices sold there are supported by an active community reporting successes or problems. This in itself might be the biggest help in getting your touchscreen project up and running.