Generally, I judge the weight, the finish (anodized/bead blasted/etc.), and whether I can do horizontal finger grinds on it ;D
Just weight and colorway. Gap profile doesn’t really matter to me.
Since I am still fairly new to throwing, I am still watching for yo-yos that could potentially add something new to my collection. Another way to put it is that I am still exploring what I like in terms of shape, weight, width, etc. Right now shape and weight are the biggest factors for me.
Well that and colourways. It is always to have something that looks cool.
“Ohhhh, shiny!” 
I’m flexible on shape, whatever looks interesting.
Color, weight, and weight distribution however is key. I like weight placed on the outer edges as I like my stability 
Color way is my most important, needs to be blue or silver.
I like variety. If something looks good and has good reviews, it interests me.
I like them all!
i look for a few main factors…
-cost. if my money had the power of a pokemon, it would be a lvl 1 magikarp that only knows struggle. because its super real. because i have no money.
-spin. i do combos that are loooong and still growing. this is why i luv oversized yoyos, because i can push em fast, without losing too much spin and being able to bind afterwords
-size/weight/specs. i like it solid, yet able to go fast when needed, ^^^, i also see what bearing it comes with, (preferably centering, but im not super concerned)
-usability. could i use it to learn on? ya.
-pads. this usually isnt a huge deal, but i prefer irpads. yum yum.
-fingerspinning ability. i love fingerspinning tricks, so i prefer it to be decent at those type of tricks (again, not the biggest issue in the world. that title belongs to people who misuse the word literally)
-horizontal. i do a lot of horizontal yoyoing, so its nice to have a relatively low wall
-color. i like aqua or anything close to looking like concrete blizzard :o
-finish. not a huge deal, but that matte finish is where its AT.
i usually enjoy most yoyos that spin. for a more in detail description, look to the left, above my profile pic
Color. Green please!
Color anything other then red and black
Shape.
Design.
Cost
Metal like 7075.
Some things I look for are:
- Width and sometimes gap width
- Colorway(but that can vary)
- Shape (if it looks interesting, but not toooo interesting)
And yea i guess that’s all I can think of from the top of my head.
I certainly look at all the stats and definitely look at the available color ways but if I’m looking for a new throw, what interests me the most and what gets me excited about a new throw is the shape, I have plenty of basic v, h, or w shapes when something new and intriguing comes along I definitely take notice. For instance the new aviator with it’s big chunky but straightish rims, I don’t think I have any throw shaped like that.
anything remotely resembling the new aviator in my current collection would be the AC2 or Summit, but if you compare them there are clear differences, that’s why I’m excited for the new aviator, it’s a new shape that I haven’t played with yet.
Round.
They must be round.