the amd 64 can run both 32 and 64 bit applications and is the better price I woudlent go with the fx51 because it is allot more expensive for not too signifigant of an increase in performance though there is a noticable difference. If you want to go 64 go with the amd 64 3400+ it is not as expensive as the fx and you dont have to buy ecc registered memory etc but will offer allot of performance
as for memory a 32 bit pc can address 4 gb where as a 64 bit could have a terabite (though that wont happen anytime soon)