Since the beginning of mi.yodeya 1.0, I've made it my practice to welcome new users. I'd like to make it clear that while I'm happy to continue doing this whenever I get the opportunity, anyone else who wants to is more than welcome to also do it (as some have).
Here's the pattern I usually follow:
I wait until I see a question or answer from a new user that I think is on-topic and at all valuable. (If I'm not sure if the user is new, I click into the user profile and see if there are any prior valuable questions or answers.)
If the content is upvote-worthy, I upvote the question or answer.
I leave a comment on it starting with something like:
@user, Welcome to Mi Yodeya, and thanks very much for the [positive adjective] question/answer!
If the question or answer could use some improvement (e.g. adding a source), I add guidance to that effect.
If an answer seems too much like a comment or discussion, I add something along the lines of this formula (adapted from Monica Cellio's):
We're a little different from other sites; this isn't a discussion forum but a Q&A site, where we reserve the answer space for answers. Please check out our short [tour]. Could you please  this to more directly address the question?
If the new user is unregistered (which will apparent from the word "Unregistered" near the top of the user's
/users/[number]page), I add something like:
Please consider [registering](//judaism.stackexchange.com/users/signup-unregistered) your account, to [enable](//meta.stackexchange.com/questions/44557/why-should-i-register-my-account) more site features, including voting.
If the new user apparently doesn't have a user-defined name (i.e. their username starts with "user"), I add something like:
I suggest that you [edit your profile](//judaism.stackexchange.com/users/edit/current) and give yourself a name!
Can you  your question to make it less personal? We [try to avoid practical halachic questions](//meta.judaism.stackexchange.com/q/1734). You might also want to see "[Why is it necessary to ask a rabbi?](//judaism.stackexchange.com/q/9146)" for more info.
If there's still room in the comment, I like to encourage further exploration, with something like:
I hope you'll look around and find other Q&A of interest, perhaps starting with our 100+ other
Meta: This principle applies to meta too; we want to encourage active participation here. When a user makes a valuable meta post or comment for the first time, we should use something like the following:
@User, welcome to meta and thanks for the [positive adjective] question/answer/comment. Meta is where the community works out policy, tagging, scope, and other issues about the site, and I look forward to your contributions to those discussions.
This is more of a statement than a question, but any feedback on or suggested alterations to this practice are welcome as answers.