Growing up in a family-owned jewelry business I have seen seen many engagement rings sold, have helped friends acquire rings for their beloved, and even got one of my own. As such, I have a pretty controversial opinion on the matter- pick out your own ring! It's your hand, and you're the one who has to wear it for the rest of your life, so you should have a say in it.
While the idea of your significant other surprising you with the “perfect” ring during the proposal is very sweet and romantic, it does come with some pitfalls. What if you hate the ring? You have two choices: either pretend to love it for the rest of your life, or tell your better half and risk hurting their feelings. Neither is a good option. Why put that kind pressure on the one you love? Why is picking out a ring a pseudo litmus test for how well they know you/your style, therefore how much you are meant to be? Even if you lay out pics and hint heavily about what kind of style you want, it's doubtful the clues will be picked up on. No. It doesn't have to be this way!
If you are talking about getting engaged, pick out a special day and head to a jewelry store together. You can try on rings and see what works best on your hand and for your lifestyle. You might be surprised, as I was, that the style of ring you pined over in the bridal magazines doesn't actually look that great on you. Trying on many styles of settings, and shapes of diamond lets you figure that out for yourself. As with your wedding dress, you'll have that “aha” moment when you know you've found the right one. Also, you can get your finger sized, which means no awkward trying to force on a ring that doesn't fit after the “YES!”, and no need to make a resizing appointment later.
You will need to talk with your love about what you can afford, but don't think of it as unromantic. You're planning your life together. Money and budget issues should be discussed early and often. You want to find a ring that works for both of you- one that you can wear proudly and one that your SO doesn't need to sell a kidney to buy.
When you have come to a decision, make sure that your partner knows which ring you liked and your size. Then, it's up to them as to when to buy the ring and when/where to pop the question. You still get surprised, but your not saddled with a monstrosity on your hand forevermore. It's a win-win!