For a PC with 1GB RAM, should I install 32 Bit or 64 Bit Windows 7?

The 64 bit version requires 2GB of RAM to work. Overall 32 bit applications require less memory (and disk space) than their equivalent 64bit counterparts.

For a 1GB system, the best to do is install the 32 Bit version, unless you want to upgrade your system memory to 4GB or more in the future.

32 Bit is a clean version and works better with most of low memory systems.

Windows 7's minimum system requirements are 2G of RAM for a 64-bit edition.

System requirements aside (where 2GB seems to be the minimum for an x64 install), you'll probably find better memory performance from a 32-bit version. Any 64-bit applications that run will have a higher memory usage profile, simply because all of the pointers in memory now use twice as much memory (64 bits vs 32 bits); similarly, the native size for some variables in memory will also be affected.