You did not mention how much memory you have. In my view, if you have 8GB, I would not go to 16GB but that also depends what you do. For typical use (word processing, internet) 8 on such an old machine is enough.
On the other end, if you can put a hand on a SSD (I don't think those models were SSD), that would make a difference. However, don't expect replacing a drive on a mac mini to be as easy as on a macbook pro of those years. I scrapped mine doing so - fortunately I found a shop that was able to fix the scrapped board for about $60 (according to an Apple store), and went for another 6 years. It's tricky to replace, and if your miss it, your money will have been wasted.
Between us, you don't want to put several hundreds $$ on that old mac. You could find a more recent model for that price. Just use this one for something else, give it as a gift to family member. Anything over $200 or $300 would be a waste, in my sense.
My two cents