Mart makes an exceedingly important point that I'd forgotten
Sorry about that.
As far as what a user sees there is sod all difference between 32 bit and 64 bit. The difference is 64 bit can use more than 4Gb Ram, 32bit won't even use all of 4Gb. There is no reason I know of not to use 64bit windows.
I nearly added to my last post that SSD+RAM+Win7 would be well on the way to a whole new machine, glad you're considering it. At some things your old machine upgraded would be faster than your i3 example, an SSD makes that much difference, 8Gb rather than 4 helps too. But a new processor will be a lot faster once whatever you are doing has been loaded into RAM. The biggie of course is you'd be at the start of the upgrade curve rather than the end.
I'd go with the new box, spend as much as possible on the CPU by getting the smallest RAM and HD I can then upgrade the RAM as soon as possible, plan for weeks later not months (it's always cheaper from Crucial or Scan than factory fitted). Then fit an SSD when the wallet has recovered properly.
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1978
Pageant Sprint - the rustomite, 1972
Spitfire IV - sprintfire project, 1968
Valencia GT6 II - little Blue, 1980
Vermillion 1500HL - resting. 1974
Sienna 1500TC, Mrs Weevils big brown.