64 bit processor

If I buy a shuttle with a

Athlon 64 3500+ processor should I put a 64 bit version of windows on
it?

What about if I get the Athlon 64 x2 dual core 3800+ processor, should
this really have a 64 bit version of windows

if I just put a 32 bit windows on it would I notice any speed difference
between theses processors or will the rest of the system hold it back?

thanks
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Nospam