Aria here, I'm on the Social Care team at Shopify.
I don't recommend you link your personal Social Media accounts to your store but I do recommend you create Social Media accounts specifically for your business and link those on the footer. Building a Social Media following provides Social Proof as well as giving you an audience to market to without always paying for advertising. Building an email list is important for the same reason. Email marketing is a cost-effective method of retargeting your visitors. We have a free course on email marketing, as well as Instagram Marketing and Facebook ads on Shopify Academy.
If you'd like to build trust with your customers (and increase the chance of them making a purchase), it's better that you don't appear anonymous. A well-written About Us page can help establish your brand.
It's also vital that customers can reach you when they have a question. This will increase their confidence that they'll also be able to reach you if they have an issue with their purchase. Consider the following options:
This post has more information on how to build a professional and trustworthy store. Don't forget to start your own thread if you'd like us to give you feedback on your store.