Which arduino will be suitable with bill acceptor
Define 'lot of code', the Arduino Uno has 32 KB Flash, the Mega 256 KB.
Define 'fast', the Uno/Mega are 16 MHz, the Due 48 MHz
Three switches use 3 GPIO's, shouldn't be a problem on neither of them; the Mega has more GPIOs than the Uno, but both have plenty for your needs.
The Ethernet shield are available for all three
I don't know the 'bill acceptor', add a datasheet.


Conclusion: it depends on what is lot of code, and what is fast.