We have chosen a setting through brilliantearth.com. Unfortunately they do not let you buy their setting without a diamond, or else we would have more options.
We are looking at one stone in particular, part of me goes "Oooh neat! IF!" But I've never seen a fluorescent stone before, so I don't know what to expect. On one hand, glowing under a black light is AWESOME, and twinkling blue in the sun is neat too. I DON'T want hazy, which I understand is quite rare. But this stone is going to be sight unseen so we won't really know until it arrives. But they have a good return policy! But that's a headache! 
Here is the stone's info:
Price: $3,680
Shape: Round
Carat Weight: 0.62
Cut: Super Ideal
Color: G
Clarity: IF
Report: GIA (preview upon request)
Measurements: 5.50 x 5.46 x 3.41 mm
Polish: Excellent
Symmetry: Excellent
Depth: 62.2%
Table: 56.0%
Girdle: Thin - Medium
Culet: None
Fluorescence: Strong Blue
So, as you can see the cut and clarity are about as good as I'll ever see on this budget! The color is alright, but truth be told I've never personally seen the different color grades compared, so G might be awesome to my untrained eye.
On the other hand, if you don't think fluoro is a good thing for me, what stone on brilliantearth.com do you think would be a good deal for under $4000?
OR, if asking about a particular other site is against the rules, could someone help me find a setting similar to this (no halo!) with a good diamond, topping out at a total of no more than $5700?
And I feel like I need to explain why I'm so excited about IF clarity... I have a geology degree. I've never studied gemstones exactly, but something that the earth produced so perfectly is really amazing to me. I think it would be really special to own, and I think I would get a kick out of nerding out and explaining fluorescence to observers too.

Here is the stone's info:
Price: $3,680
Shape: Round
Carat Weight: 0.62
Cut: Super Ideal
Color: G
Clarity: IF
Report: GIA (preview upon request)
Measurements: 5.50 x 5.46 x 3.41 mm
Polish: Excellent
Symmetry: Excellent
Depth: 62.2%
Table: 56.0%
Girdle: Thin - Medium
Culet: None
Fluorescence: Strong Blue
So, as you can see the cut and clarity are about as good as I'll ever see on this budget! The color is alright, but truth be told I've never personally seen the different color grades compared, so G might be awesome to my untrained eye.
On the other hand, if you don't think fluoro is a good thing for me, what stone on brilliantearth.com do you think would be a good deal for under $4000?
OR, if asking about a particular other site is against the rules, could someone help me find a setting similar to this (no halo!) with a good diamond, topping out at a total of no more than $5700?
And I feel like I need to explain why I'm so excited about IF clarity... I have a geology degree. I've never studied gemstones exactly, but something that the earth produced so perfectly is really amazing to me. I think it would be really special to own, and I think I would get a kick out of nerding out and explaining fluorescence to observers too.