Adjustable engagement rings advice needed!

Hello!

I'm a 25yo looking for engagement rings for my girlfriend and me. When we've discussed the matter before, she's expressed the desire that we both get a ring. I'm very unfamiliar with jewellery, and there are two main things I'm concerned about:

1. The price. We're both lower-middle class, and we don't care much for luxuries. The budget is pretty slim, but I'd still like to get something she'd love.
   
2. The sizes. We have some health issues that result in joint frequently swelling, so for comfort alone it would be better to get something adjustable.

I would love any recommendations or pointers as to where I could search for such rings, what to pay attention to, and anything worth noting for such an important decision. Thank you everyone in advance!