First of all .... congratulations!! Sure she will accept.
I agree with the second-hand theme. When you buy new, the largest part of the cost is in the design and retail value. These days there is no set design or fashion, everything is vintage and retro.
There used to be a 'stigma' attached to having a 'second-hand' ring, it was considered unlucky. That's because they only came on the market if the relationship failed, as parents rings were passed onto future new fiancees. This is no longer the case, as time changed everyone wanted new so the heirlooms were sold and proceeds divided.
I would recommed something 'victorian' as the prices are still affordable and the designs are quite ornate, if you follow women's fashion (?) you will notice we are buying copies of these designs as costume jewellery.
I wish you both well.