I was one of the first french seo consultant to switch to SSL in france, i have seen a significant long tail effect in terms of SEO in a couple of weeks after i switched to it. Other french SEO agencies that followed me saw a significant jump in SERP positions too.
Only my long tail keywords were significantly affected, the "big ones" did not gain anything, but also it might be because it's a "nuclear war" on the french equivalent of "seo agency"/"seo consultant" etc.. I'm managed to rank very well with "french seo agency" on an international level, and i don't think i would have succeeded without https, it gave me that little extra ounce of power i think.
You can have part of your site in https and some other parts in http. But beware, google considers https and http like 2 different sites, so make sure to make all your 301 redirect properly else you risk of losing lots of link juice and then your positions...
I would say keep it as simple as possible. We are experienced in resolving the issues surrounding http/https but I would rather avoid the headaches that could pop up. From what I have read, it is only incremental reward based on the work. From the Official GWT blog,
"For now it's only a very lightweight signal ? affecting fewer than 1% of global queries, and carrying less weight than other signals such as high-quality content ? while we give webmasters time to switch to HTTPS. But over time, we may decide to strengthen it, because we?d like to encourage all website owners to switch from HTTP to HTTPS to keep everyone safe on the web."
You need to install the proper plugins to do what you want to do. I have written a full tutorial but it's in french (https://www.sitepenalise.fr/passer-blog-wordpress-en-https/) i'll try to translate it, you could use google translate in the meantime.
you need the plugin :
WordPress Force HTTPS ? A Kai Armstrong
Yoast : ( force canonical to use httpS )
Hope that's enough, else let me know, i'll try to translate the tutorial today.