How do you select an engagement ring?

I got engaged on our 6 month anniversary. We have talked about it and luckily agreed that it would be a long engagement and we do not have a date set. I really don't want to have a wedding (seems so stressful), so we most likely will go abroad and elope. I am very happy about this but there's been a source of stress...

Engagement ring shopping.

I am wearing an emerald ring he got me while we search for an engagement ring. I guess I should be glad that I get to pick it out since I will be wearing it for the rest of my life, but I am not sure what to look for. I am not really a fan of diamonds and I don't want him to spend a lot of money on it. But is selecting an engagement ring like selecting a wedding dress, where there is supposedly "the one" that you know is it when you find it? Right now I like the idea of getting an antique ring but I am not even sure where to begin with that.

If anyone has any suggestions, it'd be greatly appreciated.