I'd do the hard drive but with a hybrid type if one exists sizewise. Hybrids combine a spinning drive with a solid state section for the benefits of SSD but space of spinning disk type, which are still cheapest per GB. Solid States are great but unless you compromise on overall capacity from what you had, the gains of speed may frustrate when you have to delete stuff earlier. I updated both my iMac of similar vintage and a 2011 MacPro I use as a music storage & management device. BOTH have a full 2TB drives with full Music directories with all my iTunes music in one folder (150,000...i got lucky) and the balance of space filled with a smaller chuck of my larger Grateful/BobDylan/VanMorrison/flacs etc....collection. Bigger, faster, stronger cpu's as I go forward keeps helping. Rest is space management.
Having space is key on that laptop machine. It is also slightly faster than before and never lags as before with iTunes running. (ITunes sucks anymore;I use JRMedia) I bounce between programs, depending....flacs' or mp3's? Hmmm....which today?
Anyway, also....swapping drives is easy. Buy a small screwdriver set, the little graduated slotted/phillips type with 6-7 little ones in a plastic organizer box....eyeglass repair size but longer...really smallish phillips for sure, though. DO ✔. But then do measure thickness of your existing drive FIRST (mine was 12mm max) as you only have so much thickness available. And, a 2.5"hydrid is maybe harder to find now in a size you'll like.
Alternately, adding RAM and use a newer, faster 3.0 outboard USB drive for all data (even though on 2.0 port, still faster than older 2.0 USB-type drives...better, fatter buffering is better for fast uptakes. I love portable drives....fast.
Hybrid first if size available you like. Google " 2.5" hydrid drive" and stick with mainstay old school vendors WD or Seagate....double check thickness if available....rest is simple OS restore and data re-do from your backup drive....you do have backup copies of everything first, right?