I got one of the cheapest fans off amazon and it works fine. They vary a bit regarding the min temp they (claim to) need to work off, but otherwise hard to see how they differ materially. Probably more important if your stove’s in a recess, which mine is not, but never mind. I find it useful as a temperature gauge, easier to read across a room than a thermometer would be!
I wouldn’t balk at storing kiln dried logs indoors, but my house is full of woodlice and spiders anyway…I usually bring in a week or so’s worth of wood to warm up round the fire and it doesn’t cause any problems.