I think you should look at what you want first before deciding on a price.
I had a certain style in mind when we looked at engagement rings. The one I wanted was a reasonable price, but not as much as we could have spent, but that was because I had my eye on a wedding ring that cost the same amount.
My sister got an engagement ring perfect for her that was a lot cheaper than her DF was planning on also. It really is about what is right for you.

ETA - You can always get your ring insured. All mine are insured. If it is under $2k(?) you can put it on your contents insurance.