Different editions (Home, Pro Ultimate etc.) make a tiny difference but very little.
Different Architectures (32 bit, 64 bit) have much more of an impact.
I recommend 32 Bit unless you want to use more than 3.5 GB of RAM then 64 bit is for you.
But let's be completely honest. These days, processors are WAY ahead of our current Operating Systems. Even the weak ones can handle just about anything concerning everyday needs. Windows 7 will well run on a Pentium processor as long as it has at least 1GB RAM. Unless you need a really fast processor for something specialised like video editing, large programming projects or bloatware (lol.) then you will get a much larger performance hit from buying a high quality hard disk or a solid state.
Just my two cents.