Another vote for moissanite. It’s gorgeous and strong and not expensive.
Don’t look for “engagement ring” if you are looking for ruby or sapphire or emerald, just look for “emerald ring”. Also, if you find a stone you like, any jeweler can make it into a nice ring, in a style your fiancee (hopefully) prefers. So don’t worry much about the setting. If you love the stone in, say, a pendant, buy that and y’all can have it made into a ring she actually likes later.