I'm new to TCG Live. What is a good rank to try and get to by the end of the season?

You got lucky starting now because a recent update extended the Ranked season to match the full duration of the Battle Pass, giving you much more time to climb than before.

As a new player, you should definitely aim for the first Ultra League tier rank. With the current game overhaul, you don't lose any ranking points for defeats until you actually reach Ultra League... meaning your climb up to that point is completely safe and just a matter of playing enough games to win some.

That said, take your time to learn your deck and enjoy the stress free climb. Even if you can't make it there, you're still fine... the rewards aren't that good, it's more about the challenge.