You can go straight up through the attic if you wanted to. In my living room have black single wall to the ceiling into a junction box rated. Then 2100 degree double wall out through the attic and roof. That 2100 degree rated pipe is expensive. She draws good straight up
Out the wall works too
Plenty of pictures out there and an easy formula to let you know how high to run the pipe so it draws correctly. Sometimes the stove instruction book has the pictures
Straight up will draft better.
Consider problems(valleys) at roof penetrations.
Exterior 90s will need to be replaced as they tend to rust.(out the wall install)
More pipe in the house equals more heat.(vertical install)
Straight up would require a transition box at the ceiling to carry the chimney weight and switch to insulated pipe in the attic.
