Is the blockchain crossplatform? I have the full client running in a local Windows machine but I want to move it to a VPS with Linux.  Will I need to download the whole blockchain again or can I just upload the copy I have on the pc?
I believe the blk*.dat files are just the raw block data, so they should be the same on all platforms.  You'll probably have to regenerate the databases (-reindex) which may take quite a while.

Note that Bitcoin Core needs a couple gigabytes of RAM to run well, which is more than most cheap VPSes come with.  And of course the 120+ GB of disk space for the blockchain data itself.