Most distributions can run from an USB stick, but many don't have an automatic install good for that, so it may require manual install.
USB 2.0 is no problem at all, but it's simply slow, the system will run badly. USB 3.0 is fast enough, but it requires the motherboard to be able to handle USB 3.0 and a USB 3.0 driver in Linux. (there are guides for that)
8GB is plenty, even pretty desktop distros like Linux Mint Cinnamon take up 4GB, 8GB should be enough for basic usage.
I once installed Arch on a 3.0 stick, and generally what you want to do is install the system as you would on a hard drive, but ensure that all partition designations are invariable, so in fstab and bootloader they are written by PARTUUID, UUID, etc, and not like "sda1". Also ensure that you have all the drivers you may need, if for example you intend to run the system on computers with different graphics cards.
If you want to only boot from computers that support UEFI, you can simply set the USB stick high in boot order and make a small EFI System Partition with the kernel, as the kernel can be booted as an EFI executable. That, or simply use systemd-boot. Otherwise, there is a guide to installing GRUB in such a situation.
No matter what distro you decide to go with, I recommend checking everything out in Arch Wiki, as its guides and general informations are priceless.