[ Aside from the fact that this directly contradicts the item about glass area, below, I love this stove and its bizarre arrangement of vents on top. A stove is all about the channeling of hot air and the design of this suggests that this presumably is doing something very involved without it looking fake ]
I say designer here because I was tempted to buy a stove purely on aesthetics - and by aesthetics I don’t just mean what the stove looks like, but what the fire is like - I want to see, smell and hear a wood fire, its something archetypal. So here are the minimal criteria that seem to matter and those to ignore.
Efficiency: This is heresy, but you can largely ignore the efficiency providing the stove is based on newer technology when air is vented properly. A wood stove will be twice as efficient as a fire and log burning ones typically have efficiencies that vary less than 10%. You can increase the efficiency by going for wood pellets, but I personally think the benefit is mitigated by the aesthetics (unless you are talking about a boiler with an auto feed mechanism) and the fact that where I live logs are a ‘greener’ option, coming from small local suppliers. Further, and I don’t have actual number on this, but if you choose to hide the exhaust pipe (venting out the back, into a pipe in the wall) then you lose more heat than having a super efficient stove. I like the pipe to be vertical and exposed, this is what a stove is about, its not a fireplace.
Log Size: This one is kind of important, but it majorly affects the design choices for some reason - in Switzerland or France (where I get logs) they come in half meter or meter lengths as standard. Most of the more elegant stove designs take logs that are a max of 35cm, so this is one area where you are wise to cramp your style.
Glass area: I like the maximum glass to see the fire, and prefer 3 sided glass options over stoves that rotate so you can see the fire. Note however that this will be more work - self cleaning glass has a limited ability to live up to its name when you produce charcoal next to it. I also like to be able to leave the door open occasionally (not efficient, but sometimes nice) and you can’t do this with all stoves (I don’t know why and would love if someone could clarify).
Thermostat Control: Most modern stoves have some sort of burn control but not all, so look out for it. A wood fire wants to burn quickly and fiercely, so having some control over this is a really good idea - my advice would be to only go with stoves that have a proper thermostat.
Heating Volume: This gives you one number to concentrate on, based on a combination of efficiency and Wattage and related to something that directly relates to the design of the building you are putting it in.
Double skin insulation: If you have kids you probably want something where the sides won’t burn them if they touch it.