To be honest, I feel like this question is kind of missing the point a little bit.
SEO can either be defined as the technical, all-encompassing field or strictly technical optimization. Either way, I think you're kind of looking at this in the wrong way.
The whole point of Google's algorithm updates, every update, is to weed out spam and produce higher quality websites for users. Delivering them the intent of their query. The more well designed a website is and the more relevant to the intent of their original search query, the better you're going to do. That being said, each of these metrics is pseudo-important to SEO for different reasons. I wouldn't focus on one. Instead, try to focus on what each one is telling you. @Prasad and @RanjanMishra make good points, but I'm going to go a little deeper.
Visits - This is overall how you're doing. Not the best metric, since you can't really affect this directly. It's going to be driven by whether or not you meet your users' needs and that will influence how well you rank in the SERPs.
Pages / Visit - As Prasad said, this is a fair metric (but not the only one!). Basically, the more pages your users look at, the more you are hopefully addressing the needs they have. Google tracks at how long users stay on your pages and the general structure of your website. If users spend a while on your site without going idle and look at stuff on each page for more than a minute or two, it assumes they have found something valuable. Careful, though, it may also be that people are having trouble finding what they're looking for. Which leads us into bounce rate.
Avg. Visit Duration - As I've said, Google tracks how long a user is on your site. The best possible thing is the user comes to your site, finds what they need after a few minutes, and closes their browser or moves on to something else. Unless you're a news site, you don't want users on your pages for 20-30 minutes, but 1-2 minutes is usually a bad sign, too. Depending on what you do, this is hard to gauge, but I'd say it's pretty important.
% New Visits - At the moment, you have so few visitors, it's really hard to judge this. You don't want 100% new visitors because it means no one ever finds what they're looking for on your site, which is bad for how you'll rank in the SERPs. On the other hand, if you have 100% returning visitors, it means you're not ranking well and can't attract new users and grow your site. It's a delicate balance. I'd say 30-40% returning users is a good balance, but that's just me.
Bounce Rate - When looking at bounce rate, the worst possible thing is someone spending a bit of time on your site, hitting the back button and re-writing their search query. If they looked for 'red kids shoes' and your site sells red shoes and children's shoes, but you don't have any red kids shoes, that's bad. It means the user will get frustrated, go back to Google and type something like 'children shoes in red' or 'red kids sketchers' or something similar. This proves to Google that you DO NOT HAVE what the searcher was looking for. The more this happens, the worse you'll perform for certain queries. This is why bounce rate is important. Like @Ranjan said, you should definitely pay attention to this. The lower it is, the happier your users are. The happier your users are, the better you'll end up doing in the SERPs.
Like I said, I don't think these are strictly important or good metrics for the technical side of SEO, as in what you've optimized, but it is good if you consider the SEO definition of 'a good site users want to be on' which makes Google happy and generally leads to better ranking. Hope that helps!