Wow, always turns into a one line fest of unhelpful posts. Back to the OP first;
In my own experience as a webmaster, I have seen traffic from search engines converting faster as compared to traffic from social media. But i have heard and read so many articles emphasizing on use of social media as a good online marketing channel. While I am not dismissing this I know for sure search engines work best.
First you need to separate how you view each aspect of online presence. For general sites (products and services) you will always see a higher conversion from search engine traffic, with the exception of sites like Moz, BBC news, YouTube etc as these are primarily content driven sites where the content is the 'product' as such.
The reason most of the converting traffic (purchased, got in touch) comes via search engines is because the user is in an actively seeking state, they want to buy / hire / find a review / get a quote on 'X' product or service, often near 'Y' location, but the key part here is that they are actively looking. When it comes to social media and channels such as Facebook, YouTube, Pinterest etc then the visitor is usually in a passive mode, just browsing or keeping up to date with their friends, not actually looking for anything in particular.
So which works best? It depends on the website / brand you are working on, there is no textbook way.
Onsite optimisation for social media should include unique og, twitter card etc data creating so when someone shares a link to your site on any platform it looks crisp with a cover image, title, description etc. This doesn't require that a client is active on social channels for this, but it does give them a professional finish if someone else is active on their behalf.
Always recommending social media is as bad as always suggesting a client should have a blog, it simply boils down to the client industry and also how active a client is going to be, bar outsourcing the work. So often clients get inspired at the start, then next thing you know their last blog post or tweet was back in 2015, consistency is key to both.
Social media however is unique due to the passive behavior of the potential site visitor. You have a chance to interact with your clients and keep them up to date with your latest products, services and business news. The beauty of social media is the client has already shown an interest in your brand, and since most friends of friends are into the same sorts of things when a follower engages with your posts then they will see it too, growing your circle and brand awareness.
So what to post? Again it depends on website / business / brand. Real life example is a client of mine is a specialist garage and tuning company. They have around 500 followers on Facebook. They post about cars they're tuning, link to their latest tuning showcase, add photos from around the garage, even a photo of a mole who was found asleep in the corner of the garage (probably the most engagement in a single post ever, was cute). They now get daily messages with requests like "Got a clunking noise coming from ... took it to main dealer who can't work it out" to which they get quite a few clients popping it down to be fixed, they also have quite a few reviews now, all 5 star. This is social media working for conversion, many of the messages they get are friends of an existing client of theirs, work they would not have got had it not been for social media.
Secondly because they showcase their work with step-by-step photos and videos (upload and linked to YouTube) of the cars after tuning they also have a lot of their content shared more via image based channels such as Pinterest. The people sharing them are all car fans, who's followers / friends are also car fans and into tuning, and so this circle grows, and they get work requests like "I saw the 300bhp stage 3, I own a ... how much would it cost?".
Finally, does social media have any impact on search results? A little. For example a search for a company name will often also bring up their Facebook, YouTube channel etc under their main website. I also think that due to search engines knowing so much about the content being shared on these channels then it would be a signal of some sorts, again they might take into account social media review ratings and blend it into their algorithmic mix, but I wouldn't say that the serp outcome of your domain would change that dramatically unless there was a breaking news storm.