1) Intel has by far the best support, but not the best performance. AMD is a mixed bag, but improving. NVidia has poor open source drivers but solid proprietary drivers that are quite good, but are not always easy to install in all distros. I recommend NVidia if Intel won't work for your application.
2) With Intel most distros will configure themselves correctly (debian, ubuntu, or Mint should be fine and have robust MC support). If you opt for NVidia you'll need to install the proprietary drivers on most any distro (most don't ship the proprietary drivers for licensing reasons); it's relatively easy to install them on, say, Ubuntu or Debian, a bit harder to install them on soemthing like Fedora.
3) I haven't encountered a distro that doesn't automount external USB NTFS drives on boot or on hotplug; it's pretty standard these days with full-fat desktop environments. If you do some kind of "minimal install" you might not get automounting, but otherwise it should just work. The only question is whether it automounts them in the same place each time (some distros seem to do that successfully, others not so much analogous to drive letter assignment in windows). The easiest way to fix that in any distro is to edit the filesystem table (fstab) to assign a mount point for disks by UUID, but there may be a GUI tool to do that out there if editing the file sounds daunting.
The nice thing about Linux is that there's no "registry"; almost all configuration is in plain text files in various places. The hardest part is knowing which file you need to edit.