Having plenty of wood stove experience, try not to run the chimney on the outside of the house if you can... obviously sometimes it just has to happen. Chimneys on the outside naturally flow in reverse (outside chimneys have a natural flow of cold air coming down them into the house). Trying to get a fire going with air flowing down the chimney is difficult and often very smokey. My aunt with an outside chimney used a hair dryer pointed up the flue to get things going in the right direction and then she could light a fire without smoking herself out. Some people light pieces of paper and jam it in the flue to get the flow turned around before they attempt to light a fire. It doesn't matter masonry, stainless, insulated, all outside chimneys experience this it's physics (though some suffer worse than others).
Because of the same phyics chimneys on the inside of the house always have flow in the right direction which makes starting fires easy and burning great.
Usually todays stoves don't recommend (or may not allow) single wall pipe. Often the reason is because todays stoves are so efficient they let just enough heat escape to create draft. Approx. 80% efficiency (combination of combustion efficiency & transfer efficiency) is the maximum a wood stove can be without needing a fan to supplement its exhaust. They once made an 80%+ efficient wood stove but it no longer let enough heat escape to draft. They added a fan to the exhaust but eventually canned that idea it was extremely difficult to figure out how to moderate the fan speed since burning wood is so inconsistent and their research showed no one wants to buy a wood stove you have to plug in for it to work... their claim to fame is they don't require electricity. Instead they modified it to let more heat escape and it started naturally drafting. That's why there isn't stoves over 80% total efficiency (combo of combustion & transfer) they tend to be 72-75% and why pellet stove being over 80% need a fan to exhaust (their burn is controlled so it's easy to figure out their exhaust fan speed to the rate of feed).
Anwyay, the whole point is todays stoves only let enough heat escape to draft and single-wall pipe can reduce the amount of heat escaping out the chimney below 20% and cause poor burning, draft & creosote issues.
I should also add that the warmer it is outside the lower the power of a stoves draft since it depends on temperature difference. When it's 5F outside stoves burn & draft great even single-wall ones but if you want a fire when it's 50F+ outside you need as much draft as you can muster. That's when a single-wall pipe or/and outside chimney is really gonna cause trouble and you may not be able to get a fire going. Chimney height helps with that (the taller the chimney the stronger the draft so extending your chimney may let you burn when it's 50F+ outside if you have troubles). Catalytic converter wood stoves hinder draft and usually not recommended with outside chimneys. Probably more info about wood stoves than you ever wanted to know *
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