My husband and I got engaged 26 years ago, just before he was headed back to his home base out of state.
At first he wanted to propose with a cute little ring - turquoise hearts. While it was really cute, I pointed out that no other guys would think I was engaged if I wore it. I knew he couldn't afford a super expensive ring and wasn't asking for that, but I did insist that it needed to look more like an engagement ring. Enter a cheap cubic zirconia type one for me to wear.
He ended up surprising me by buying a true diamond engagement ring with a more formal proposal before he left. To this day I still love it.
I went cheap on the wedding, doing a ton of things to save money since we were paying for it all ourselves - no alcohol, morning ceremony, afternoon wedding, inexpensive bridesmaid dresses that they could wear again, etc. But there were a few things I refused to cut costs on: 1) the photographer, 2) the dress, and 3) the ring. I wish now with hindsight I had gone cheaper on the dress (spent about $1200 if I recall - cheap compared to what many spent on wedding dresses back then, but way more than I needed to spend for something that would spend the rest of its life in a cardboard mausoleum box in the closet), but I never for a moment regretted that we spent good money on the photographer and ring, both of which were the permanent mementos of that day. 26 years later, I still wear my engagement/wedding ring every single day. It is still as gorgeous today as it was when he gave it to me and it has increased in value from when we bought it. THAT I consider money well spent.
I think we spent about $1200 total for the rings (hard to remember if that was just for mine or all three as we got one for hubby as well).
Like most things in life with me, I go cheap on the parts I consider disposable or that I don't care about, but I spend on the things I want to last a lifetime.