I'll mostly spare you the financial advice, but it's worth thinking long and hard about spending a huge amount of money on something with almost no resale value, whose price is artificially inflated by a global cartel, which is actually just a semi-precious stone, and which is indistinguishable with the naked eye from far less expensive alternatives.
As for aesthetics, a further warning is that in my experience, whenever someone says they want something unique, not just in fine jewelry, but also in clothing, interior design, etc., they usually know very little about whatever it is they're buying. That's a problem because, as is often said, you have to know the rules before you can break them. That's especially true when you're buying for someone else.
That said, consider emerald cuts, and colored stones if you want to be different. There's a reason people typically go with round-cut solitaires, though. It's because they're gorgeous little orbs of light that stand out from across the room. Lately people have been into halos of smaller stones around the main stone. This adds some sparkle and makes the stone look bigger, at a cheaper price. It's such a huge trend that I think it will look dated eventually. You can also look at having pave stones all around the band.
If you really want to be different, look at estate jewelry from the first half of the 20th century. (It isn't "used." Cars are "used." Old jewelry is like art. You wouldn't call the Crown Jewels "used," would you?) there is some beautiful stuff from that era. It's relatively affordable, it's socially conscious, and it demonstrates taste and an appreciation for history. You can get it cleaned and polished by a reputable jeweler so it looks like new. You can even replace the stones on a historic setting with modern stones (which are more brilliant because of superior cutting technology).