Engagement Ring Advice

You should try the rings on your hand. If you cannot, then have your mom do it, or someone with similar hands and fingers as you. It's very hard to tell how a ring will look on your hand. Someone with long thin fingers is going to want a different style from someone with thicker fingers. Additionally, the color of your skin will make the ring look different. As a Japanese woman, diamonds that are even slightly yellow look even more yellow against my skin whereas darker skinned women tend to make yellowish diamonds look whiter.

Also, since some of those pictures are stock photos, there's no accounting for the diamonds cut, clarity, carats, and color. (and the elusive 5th C, 'certificates').
Based purely on the pictures, I like the third one. Single solitaires are my favorite.

On a different note: Are you an only child or are there other sisters/cousins in line for the other rings? If so, ignore this suggestion otherwise if you are the only one I would work with a jeweler to combine the rings. You can sell the metal back to the jeweler to offset the cost of having them reset into a ring combining stones from each ring. The stones that have matches can be made into earrings and the remaining stones can be set into a necklace or bracelet. I only ask because I'm in the same position as you, I have several wedding rings to chose from. I decided (with my grandmother's blessing) to remove the stones and have them set into my own band. The remaining stones are being turned into earrings, a necklace and a second right hand ring.

My final suggestion: I know you want to get the process started but my recommendation would be to WAIT until you can get the ring in person or someone you trust can courier it to you. The last thing you want is for it to get misplaced because you couldn't wait 5 months. Then you'll have all the rings in front of you and you can talk to a jeweler or gemologist that can tell you what they recommend. This ring will be for the rest of your life, what's 5 months?