When I look at the 'First Posts' queue, if the question is topical and sincere, and somewhat decently composed, I will always up vote it. I never down vote anyway so that side is irrelevant. If the question is crap, I'll use 'Skip' and close vote it off the question page itself.
Now I have noticed that other reviewers are not using the same criteria as me on 'First Posts'. What do you do when you review a 'First Post'? (on the main site, not here in META)
I agree with your review approach, apart from the fact that you shouldn't skip the review if the question has something wrong with it. See a missing tag in a question? Add it. Title is not informative enough? Enrich it. Is the answer missing some fundamental information such as references? Ask for some. Post is unfit for TSE standards? Flag it.
Downvoting is in my opinion a way to tell the SE cleanup bots here's a low quality post, might want to add this in the relevant queue. I usually both flag as spam and downvote to make sure the post stands out more and is removed quicker. But I rarely down vote low quality questions. As you say, let's give new users the benefit of the doubt. Having said this I'm usually very quick on the off-topic, duplicate flags and the like. Catching these posts early is in my opinion the best way to maintain a high quality SE site.
Skipping is to be used when you are not sure and want someone else to handle the matter. I usually skip detailed visa questions for example, because I know nothing about visas.
Main reasons behind adding "first posts" in the review queue are:
Spam, spammers are usually people who create new accounts and then post some spam, so this queue can help in filtering that. Actions: [Flag] it as spam, downvote if you wish as the automated bots do clear things depending on the flags + downvotes.
"Sincere" new users who ask for the fist time, usually they are new to the SE platform and the way we run things here, so the queue can help in putting things in track before they pile up and ruin the whole spirit of SE. I personally think of it as private lessons to these users who didn't bother to read the Help before they ask. Action: [Edit] in case it needs to be reshaped to fit in, or [Flag] it in case it is off-topic, broad, etc.
Please note, you still can add comments, and that's an action, try it, and once you add a comment the review buttons will change and show the [I'm done] button.
Clicking [Skip] is not an action, [Skip] button was meant when you are not sure what to do, so clicking skip will give the chance to someone else to look at it. Always click [I'm done] after doing one of the actions (flag, vote, comment, vote to delete, etc.) or click on [Looks OK] if the post is ok and needs no actions. Clicking skip will not add to your review achievement.
Regarding upvoting, use your normal upvoting criteria. Personally, I would upvote new users when they ask a new question just as a welcoming gesture, as long as the question follows SE standards. I never downvote new users, I prefer giving them the benefit of the doubt.
Provided you have votes available, if the question shows research effort, is clear and useful then upvote it and if it does not show any research effort, is unclear or is not useful, downvote it.
As I already earned to gold badge for first post reviews, I always click on skip after reviewing the post - so that someone else also have a chance to review it.
It's possible that there is something wrong with a post and I don't see it, but probably the next reviewer will see it and handle it. We don't have so many new posts to review and I think it's not ideal that a review is completed after only one "looks ok" vote.
