Infrastructure upgrade for a small organisation

Hey guys,
my organisation is planning to upgrade from the 5 year old server we're currently using. I am far from a network expert but I do know a thing or two about computers generally. The current server is unfortunately a bit too laggy for our needs (still runs on HDD-s, 16 gigs of RAM and an Intel Xeon E5-2620 v2). It is used as a remote windows desktop for around 30 users, of which no more than 5-10 are connected at any given moment. We use it mostly for basic office work so the workload isn't all that huge.
My question would be if this hardware is completely outdated beyond use or would it be possible to swap out the HDD-s for SSD-s, slap on some RAM and keep on using it for another few years. If not, what would your recommendation for a new machine be?