64-bit and 32-bit (the latter is also called x86) refer to your system’s CPU architecture. Most modern PCs are 64-bit, but some 32-bit systems are still being made, generally as low-end and budget computers. If you aren’t sure which you have, the 32-bit version should run on either kind of system. More info.
As to whether to get the browser version, you can if you want. If those MBs are valuable to you, the browser version is serviceable enough, I think.
If you’re on a limited or metered connection, note that the game is receiving an update on the 20th. As to whether that’s worth waiting for, that’s up to you. The updated version is going to be rather large, about an 80 MB increase across the board on every version.