Your comments are very welcome. I did not expect to get such a long and good explanation. I have a degree in electrical engineering and learned the basics of electronics in school 15 years ago. My career took a different path, I now work for an engineering company as a safety advisor.
Yesterday evening I soldered an LM2576 and the necessary components to a PCB and did some testing. I first attached a couple of leds, and measured almost exactly 5V powering it from my 25A lab power supply with only 7,2V. I then started attaching some 2W resistors till I got 2,5 amps out of the regulator. The voltage dropped a bit to 4,89V, which is still acceptable. So the cheap China inductor is up to the job
I did not expect anything else as I did a lot of googling before I bought them. I found several people that have used the same inductors from ebay with the LM2576 regulator. The LM2576 can be found very cheaply, I paid 0.58$ a piece.
As for the board: I've decided to ditch the ICSP header as I will never use it. I don't have a programmer to connect to it. I only need the ftdi header to upload sketches and use the serial monitor. I've already bootloaded a couple of ATmega328's on my breadboard, which was very easy. I've also decided to leave out the led on pin 13 and the small inductor as it might cause more issues then do any good. I've added a ground plane to the top of the board and made most traces a lot wider, especially the VCC and AVCC connections. I've attached 100nF caps to both those pins. I'm going to leave all the big caps on the board. From experience I've seen that they are helpful when you power a lot of servos.