SSD upgrade

Hi, 

I currently have a 15 5570 and I'm looking to upgrade to an nvme SSD. I'm aware that I can only go as high as 512gb but my question is and apologies if its a stupid one, I'm not good with this stuff, can I use both the stock hhd and the new ssd? 

My problem is I currently have about 6-700gb used on the hdd so the 512gb is going to be an issue.

Could I just move the important stuff to the ssd so the machine would run faster?

Also, would I benefit from adding another 8gb of ram? 

I use the laptop for music production and a small bit of gaming but nothing serious. 

Thanks in advance