As lg said, Debian would likely be slightly less hassle to make "minimal" if you start from the base install plus SSH (which is what most VPS providers give you as the starting point), though if you are already familiar with one of the other options I would go with that instead.
Some code segments and data structures end up taking more RAM in 64-bit code than 32-bit which might make a difference, though I expect that difference to be small. You are given the choice because 64-bit CPUs based on the amd64 instruction set (i.e. current AMD and Intel offerings, with the exception or Itanium and related chips if those are still generally available) can happily run both 32-bit and 64-bit code together with minimal overhead so in most virtualisation systems a host with 64-bit CPUs can happily run VMs with a mix of 32- and 64-bit OSs at the same time.
In only 256Mb RAM you will probably need to tweak the Apache and mySQL config for efficient operation, though there are plenty of decent guides for that out there. Tuning mySQL (and Apache) will make much more difference than what Linux variant you go for.
To reduce your compatibility issue concerns just keep to the packages provided by your chosen OS, this will also save you time and hassle when security updates are released.
If you are not particularly familiar with any of those Linux variants I strongly suggest that you "play" with a local server first before trying to setup a public server. Install vbox (or vmware or similar) and create a few 256Mb VMs, one for each OS you want to try, and give them all a look. A local server in a VM like this will mean you can play to learn the ropes without worrying about being charged admin fees to rebuild the VPS if you break something significant, and such a VM will also provide you with a useful testing environment for when you are planning changes to your public server and the services it runs further down the line.