What power tool is the best and fastest to take up floor tile?
A rotary hammer with sds plus attachments will likely serve you best.  These tools usually have three functions:  hammer (with a chisel bit for your purpose), rotating hammer (for drilling through concrete), and drill.  The tool plus the chisel attachment will run you about $300.  I've found mine very useful for the odd jobs of removing tiles and drilling for anchors.  They can be found widely at home improvement stores and online.