I am planning to start working in some yet not chosen distro of Linux. My plan is to buy an external drive for my laptop running Windows 10, burn the iso image in the external drive and boot from there. My specific question is: after booting from the external drive, when Linux offers me to install, would it install in the external drive or it will attempt to install in my hard disk. Or it will give me the choice of the drive where to install. The distros under consideration are Ubuntu, Mint or Debian. Also, what transfer rate the external USB drive should have for Linux to operate efficiently. Thank you for answering!
An external hard disk drive or SSD connected via eSATA or USB 3 will work well with linux.
A hard disk drive or SSD will work also via USB 2, but of course slower. USB 2 pendrives will be even slower, because of slow flash memory hardware. See this link about speed of USB pendrives. It is also possible to use a fast memory card.
It is possible to do what you suggest, but it is much easier to get a USB pendrive as an intermediate tool, clone the iso file into the pendrive, and boot from the pendrive.
It makes the installation to the final target drive (hard disk drive, SSD, fastUSB 3 pendrive or fast memory card) both easier and less risky, if you disconnect or unplug the internal drive with Windows during the installation. Then you can write the bootloader to the external drive, and it will work on its own.
That Ubuntu system will be portable to other computers, if you install no proprietary drivers.
Boot via the internal drive
If you do not intend to make a portable drive, but only intend to use the external drive in one computer, you need no bootloader in it. In this case it might even be more convenient to boot via the internal drive. In this case you need not and should not disconnect the internal drive. But check and double-check, that you install Ubuntu to the correct drive!
If you use a pendrive or memory card for your installed system, you should tweak the system, to reduce wear of the memory cells.
So to do this you want to plug in your drive in while the computer is off then put in the installation medium. Then in the bios change the boot order to boot to the medium first. Most BIOSs are accessed by pressing The delete key or the F2 key THIS IS DIFFERENT For every motherboard. Once booted into the medium when asked where to install ubuntu find the drive that is external it should be under /dev/sdb
Once you have installed ubuntu on the computer you want to use it on change the boot order to boot to the external drive first.