Definitely, move it to Siteground servers.
I vouch for SiteGround. Want to know why?
Here is why.... http://www.onlinemediamasters.com/siteground-wordpress-hosting-review/
I vouch for siteground. But I currently use 1and1 hosting. Because its very cheap and offers free ssl. Plans start from $12 first year and other years $108
Already moved to SiteGround. The support is blazing fast and amazingly helpful. Thank you @Ammz for leading me to it!
Don't forget to create a free account on cloudflare if you dont have one already, and activate it via your siteground control panel to speed up your website. Download the supercacher plugin by siteground and activate that too. You dont need w3 total cache plugin when you're using supercacher.
1) Since my website now has SSL support, enabling Cloudflare wouldn't cause any issues, right? 2) I still have WP Super Cache that was restored while site transfer, should I disable it too if I am using SuperCacher?