Definitely ask for the parent's permission (actually her father's permission), if she is still supported by them (lives at home, they pay for school, etc). If you've been dating her for 5 years than you know him really well anyway, nothing to be afraid of. It doesn't matter if they say no, you'll ask her anyway. It does matter if they say yes - they will be your in-laws for life, good to get it started off right. If she is out of the house and independent, then its a formality that may or may not apply, you can look in your heart and see.
IMO, the cost of the ring is secondary to the 'uniqueness'. Women love to have a ring other women will grab and say 'ohhh', it's so beautiful or special or whatever. For some that is exotic tension settings, for other's its platinum, for others its a neat braiding or pairing of two rings. If you've know this woman for 5 years, you should for sure know her ring size (try her rings on your fingers, note where they stop - you got it) and also know what she likes as far as taste. If not, well, you may be in a bit of trouble getting married. She wants you to love her for her individuality, and a unique ring or special 'inside' knowledge shows her that is what you love.
I proposed at our special place, which is near Ballard Locks in Seattle, on one knee, with champagne and glasses hidden nearby. We were completely alone.
Good luck