... But I can tell you what I know. Coal stoves, pellet stoves, corn stoves, and the like, have relatively no problem to 'healthy people'. BUT, those people whose lungs are easily affected by even household dust or pollen, will have a problem with these types of stoves. As you point out, it's the dust; not the burning.
As for ventless gas stoves, the problem DOES come from the combustion process. Even though 'they' say that venting the burnt gas into the house directly isn't a 'problem', it IS for those people whose lungs might be sensitive. So again, even this type of stove has potential drawbacks.
So, where does that leave you? There are a couple of options. You could consider installing your unit in the basement (if you have one), and put in floor vents so the heat can rise 'up'. This way, the dust and such is confined to a completely separate area in the house. Granted, this setup isn't perfect. Some dust may make its way 'up' but I don't think that the dust levels are as high as they'd be if the unit was in the Family Room. It's a relative thing, you see. ANd if the unit has an automatic feeder, you can reduce the number of times you 'feed' your unit, thus, possibly reducing the amout of dust you create.
YOu can consider a natural gas or propane stove that uses fresh air from the outside AND VENTS to the outside. This way, the house air isn't 'stolen' to operate the unit, nor are its gases vented into the house. These days, energy efficient homes are having this type of 'venting' being built into 'locked' fireplaces. Yes, that's right, the fireplaces that you put logs into! You open it to 'feed' it and when you close it, the oxygen source is 'inhaled' from the outside. Of course, this means that the fireplace has a sealed door and you really can't leave it/them open. (Otherwise, you'd defeat the purpose of the outside oxygen source, and suck in already heated air from the house, and probably cause a hazard if the outside 'vents' were to create back-pressure.) Trade offs, you know?
Keep shopping around and keep asking questions. IMO, if I were to get a stove, I'd get a natural gas one whose oxygen source is from the outside and whose vent system is TO the outside. I'd also get one with 'blowers' to help push the air around. And since I'd only use it in the Winter, I'd like to be able to disconnect all that 'plumbing' so I can put it away in the warmer months. Wouldn't that be nice!
That's all I have. Happy shopping (and learning.) YOu'll be very informed by the time it's all said and done. My best to ya and hope this helps.