Should I upgrade my RAM or replace my platform first?

You should prioritize a platform upgrade over adding more DDR3 RAM. 16GB of DDR3 is still usable for most things, and spending money on 32GB for an old platform is a dead end. Save that cash for a new CPU, motherboard, and DDR4 or DDR5 RAM—the performance jump will dwarf any RAM upgrade. Unless you absolutely need 32GB right now for heavy workloads and can’t afford a full upgrade, don’t bother.