Installing Fedora onto USB drive - potential bootloader issues?

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I wish to install Fedora 25 onto a USB drive as if it was a hard drive, so that I can get a portable Linux setup with full persistent storage. I'm a bit concerned however with how this works alongside the bootloaders of whichever machines I end up using it with.

• If I install Fedora as I would to a hard drive but simply target the flash drive instead and do a regular setup, will this drive be bootable on the majority of systems? (UEFI/BIOS, existing Windows/Linux installs etc.) If it depends on whether the machine I install from happen to be running UEFI or not, which would be the most advised for compatibility?
• When Fedora occasionally updates grub, will this mess with the local machine I'm running the drive in? I'd really not want anything to happen to the bootloader or firmware of any system I'm plugged into as the point of this setup is to be able to use the USB drive on a variety of computers.
• Would it be better to simply install as a liveUSB and use persistent storage through that method? This seemed more complicated and less flexible when I read into it on the Fedora wiki, but if the above issues are significant maybe that's the only approach that makes sense.

Would appreciate any help and feedback here! :)