Wow, this thread was only around 2 hours ago... you made a quick decision!
Did she mention why she wanted a ring? A ring is my favorite form of jewelry and I think rings are one of the more common favorites, but I don't care too much about the 'realness' or anything. I just care that it does not break... I've had cheap gold rings before. They may be coated with gold and I've had them just flat out break from no effort whatsoever. :( I didn't know any better, I just liked the design...
There are girls who like to wear jewelry for the sake of jewelry... for example, a goth girl may love silver, and they like to have all their fingers covered, their wrists, hands, neck, ears, etc...
There there is the 'bling bling' girl who wants something that makes her feel special, helps her stand out around other girls, that also holds value well. Something she can show off to other girls and that people will take notice and ask her about it... that type of girl is more likely to be little more superficial, care how many karats, things like that.
I'm in-between somewhere, not a huge jewelry person. I told my husband not to spend too much on an engagement/wedding ring, but that didn't stop him from spending at his limit. He didn't get a $1,000+ ring, thank God, but I think he spent $500-$600 on them total. And he bragged about getting platinum because it was more 'man metal' that he said was nearly as destructible in his eyes and wouldn't get as much scratches (they still got lots of scratches though lol)...
Anyway, the best way to really judge what your girl likes is by what she already wears. Girls generally won't wear anything she is not comfortable wearing and that does not fit her tastes. If she wears jewelry now and doesn't seem to care what other people think when they ask her what they're worth and where they came from (because other girls do ask about that crap often), then she probably will not care if yours is cheaper.
If she never wears jewelry, she just may 1) want to just receive that type of gift from a boy and 2) wants to start blinging herself up more, but wants you to make the choice for her... a younger girl who is a lot less showy with her clothes, make-up, more shy is likely to be like that. It could also be she owns jewelry right now and has a jewelry box... in which case you would have to notice it in her room. Ask her why she doesn't wear the stuff that's in there. It could be as simple as her family gave it to her and it has no specific meaning to her, so she may just want something from you that has more special meaning...
Personally, I liked your first choice better. More elaborate design. But I think if it's cheap gold, you have to be careful with Ebay, because it could just be coated and it may break more easily.
Other thought, if she kept mentioning a ring but didn't tell you exactly what she wanted, she can't be too upset if it ends up being something different than what she was thinking...