I have a preference, so my point of view is slanted to that. For example, say you have prostrate cancer and talk to several doctors. The surgeon will give you a surgical perspective. One specializing in radiation will give you that perspective, accentuating the pluses of whatever slant, etc. It's not a right or wrong choice, but a what works for you. So it's up to you to do your research and choose what fits and doesn't.
Take your time and talk to lots of people that have stoves.
Find out their likes and dislikes.
-There are steel stoves and cast iron stoves.
-There are domestic built and european.
European stoves may have pluses in innovation and style, with the consideration that Europeans may cut their wood to a shorter length than is standard here. Not an issue if your doing/cutting your own firewood. It may be an issue if purchasing firewood.
-Then there are obviously various size stoves. You can burn small, hot fires in larger stoves, so going bigger is maybe better than too small.
-Catalytic vs non-cat, of what Vermont Casting calls Flex Burn, which is a choice of both in one stove.
Catalytic stoves need very well seasoned wood, or the ceramic honeycomb of the catalytic element will plug up much more quickly. They can be cleaned, carefully brushed out and (smoking) pipe cleaners or tiny brushes for paint spray guns used to poke out the crude. The elements are sacrificial and need replacing every three, four, or plus years, depending. We ordered one last month to have on hand for our stove, at approx. $200.
-How does it function, or how do you interact with it.
There are front load, side load and top load. Our first stove was a box stove. Long and narrow, front load, and burned front to back, no ash pan. Which meant when reloading, the hot coals were in the back, and needed to be pulled forward before reloading. It was a dusty stove in that respect, and ash was removed by shoveling it out and dumping the shovel full of ash into an ash bucket. Very dusty overall, no mater how careful one was. Now there are dedicated ash vacuums, however, they are very messy to empty and clean the filters. So consider loading, and ash removal. My preference is top load, with an ash pan. Do several mental walk throughs of bringing wood in, loading the stove, reloading the stove, removing ash from the stove/house.
-another consideration is flue size. 6" or 8", And chimney design.
Our stove sits in front of the chimney chase, requiring a short is of 3' from the stove top and then a 90° return to the chimney. This ruled out one stove we considered that required at least 6' of rise before a 90° bend to maintain its burn efficiency.
-Then there is looks or aesthetics.
It is going to be there year round.
Windows, enamel finishes, etc. Windows get ashed up, but self clean if the internal flow of air washes the glass when burning. Enamel is wonderful looking year round. Typically found on cast iron stoves. It can chip if you drop a top load lid, although there is touch up paints for those slips if ever needed. Black cast on the other hand needs stove blacked once or twice a heating season to keep it black and nice looking. Then the first firing afterwards often smells or slightly smokes for a few minutes.
-As mentioned above, installation with a new build has special code requirements for under the hearth, under the tile (like micor board) which is probable a trade name. Cement board, often used under tile, is not code here anymore for under wood stoves, hasn't been in over twenty years, so talk to someone who knows codes in your area.