1. Use the comma.
Welcome can function as a verb, meaning "to make someone feel welcome or comfortable." Without the comma,
Welcome Susan makes it seems like I am telling the reader to make Susan feel welcome. That's how I would write it if I was going to say, "Please welcome Susan after she arrives."
2. The period is optional.
As for the period, you can choose to leave it in or omit it. Because this welcome message is not part of a longer paragraph, there's no need to use a full stop. Your greeting works much like a newspaper headline, ad slogan, or book title: full punctuation is not required, and grammar rules need not apply. That said, if you wanted to add some level of emphasis to the message, you could use an exclamation point:
As a footnote, when dealing with short phrases, some graphic designers choose to include a period, and some don't: