Is it good idea to use up-to-date Linux on USB stick instead liveCD to online banking? What is the best Linux distribution for not advanced people who commonly use Windows to make online payments safely?
Yes, using a second separated system will protect your privacy much more like doing this kind of stuff on the same PC. You can use ANY Linux distribution for this and there could be battles over which one is better, but since you already said you are a total beginner, I would suggest you to try out Ubuntu at the start, since it's a very user friendly distro and has a big community. However, if you have a special focus on privacy, you could also consider Tails, Whonix or Qubes which are all more designed for privacy enthusiasts.
Also it should be noted that Live Systems are not really that necessary nowadays where we have huge USB sticks. Nowadays you can mostly just install the distros on the sticks directly as if they were hard drives.