You are definitely not being a princess at all!! I think the ring + engagement is important as symbolizes a lot of things that are not materialistic - your devotion and commitment to one another, among other things. It seems like more communication is needed here in terms of what each of you might want regarding an engagement - he may be avoiding it because he doesn't want to disappoint you, but it sounds like you are being very reasonable in terms of affordability right now. A conversation along the lines of 'hey you're special to me, let's do this one special thing together' could do the trick - and include your feelings about the ring and engagement, no matter the size, is meaningful to you beyond materialism. Good luck!
Just for some price reference points, I am browsing Amazon right now, and they have very simple, pretty, sterling silver rings under $20: https://www.amazon.com/BORUO-Sterling-Tarnish-Resistant-Comfort/dp/B06XPNVSGZ/ref=sr_1_9?s=apparel&ie=UTF8&qid=1534874852&sr=1-9&nodeID=9539899011&psd=1&keywords=silver
For something with a stone, I would look at Moissanites, here's an example for around $150: https://www.amazon.com/Moissanite-Engagement-Ring-size-Charles-Colvard/dp/B01LX2ZF4D/ref=sr_1_8?s=apparel&ie=UTF8&qid=1534875065&sr=1-8&nodeID=7141123011&psd=1&keywords=moissanite+engagement+ring
Hope this helps!