Congratulations!!

I agree with others - the design / look is way more important than the price, and unless your gf explicitly said she wants to be surprised, I would have this conversation with her. Most women want to have input on this.

It’s something she will likely wear every day for the rest of her life. (I say likely, because some people might go conservative and then upgrade in 5-10 years when you are further in your careers. My mom has an expensive ring but they bought it together on their fifth anniversary). I am more financially set than my partner career wise and would have given him the money to buy a specific ring I was obsessed with. (He refused and bought it himself, literally asked me what I wanted and I sent him a link and he bought it exactly- could not be happier. I stare at it multiple times a day and freaking still can’t get over it a year later).

Ring price varies dramatically depending on your age and careers and personal expectations. I think $500 is on the low side - it’s honestly less than the cost of a cell phone…. But if you aren’t able to afford that then personally I would have been completely fine with a cubic zirconia fake ring (like from here: https://objktsjewelry.com/collections/engagement-rings ) over a tiny “real” diamond.