By a wood stove, I presume it's a slow combustion heater/stove that has a firebox and glass door to completely enclose the fire. The heater outputs combustion gases through a 6'' diameter flue , with we call a chinaman's hat on top outside the roof. This hat allows exhaust gases to escape but stop rain getting in.
The point about these types of heaters is that produce a massive amount of heat, and I've had one I forgot accidentally on high actually turn the flue a bright red, all the way from the heater to the ceiling as it was an exposed flue. Luckily it had a secondary flue to prevent burns and between ceiling and roof a triple flue. The reason I mention this is that the chances of you or someone else turning the heater up high are not remote, so you have to allow for this possibility. The only metal I know that lasts and can withstand this heat is stainless steel, and you can tell it gets hot because it blues beautifully like the exhaust pipe on a Harley bike. Don't try anything else like galvanized pipe, because the galvanizing will peel off or burn off, giving off toxic gases and soon rust. Wait until you can afford a continuous (Comes in segments) stainless steel flue and protective outer sleev/s before installation.
The next question to ponder is, does your chimney have brick corbelling inside, and correct throat. For an open fire, this is critical to draw correctly and is somewhat easier to adapt to suit a flue. A flue must not be angled less than 45deg. and a maximum of two bends are allowed in its length. Aside from either the heater setting combustible material alight that's too close (children's night attire) or the flue starting combustion in your roof (which is not a problem within a chimney), correct air ciculation is critical. Fires produce carbon monoxide as much as other gases, and at a level these heaters pump out heat, its like running your lawn mower inside if the flue doesn't work correctly.
The question of cost doesn't come into it. You either do it properly or not at all. Like a gas heater, you woudn't dream of running one without a flue or the wrong flue, nor would you have one that doesn't shut off the gas if the flame blows out When gas was first introduced and used for domestic lighting, people went around with a lighted match to find a leak, making the mythbusters look like amatuers after the house and occupants were blown apart. If they didn't light a match, they simply passed on in their sleep.
Moral of all this is: safety concerns are paramount, and you must be alert at all times as you would if you were using a chainsaw or other dangerous tools. Please be sensible and do the right thing. Cheers from Oz.