Have you looked to see what the maximum RAM is for that computer? I did and it says 8 Gb so you could be wasting your money if you go for 16 Gb. Have a look at the specs just to make sure before you commit.
I second the SSD thing. It would add some speed to the experience.
If you're just giving life into an older machine, you could also install a Linux distro on it. It would give you a snapper experience and even get you updates that may not be there in Windows 7 & faster than installing Windows 10 with older hardware.
I may not even upgrade it.
Are you monitoring RAM usage in task manager? Are you maxing out or getting close? If so yeah grab another stick but a new machine is ideal naturally.
Physical Memory is at 63% or so with all 3 browsers