Had no problems whatsoever with Vista 64, no driver shortages and it certainly is a lot punchier than 32 bit flavours.
That being said unless your pc is pretty powerful (2gb+ Ram) then you might not see much improvement..but your processor (unless it's pre-ark) will be 64 bit and running a 64 bit OS just makes sense.
Programs will work fine as most install in x86 (32 bit) mode, broadband won't blink as I don't think your router gives a hoot what OS you are running tbh.
If you post your pc specs we can tell you if you may have grief with an unsupported (older) piece of hardware...or not.
Lack of driver support on a 64 bit OS was true of XP but not Vista (not so far anyway lol)
Cheers
Samwise