If your flue is an old square brick one constructed as part of the wall then yes, it will take a long time to warm up and condensation will be a problem no matter how dry your firewood or smokeless fuel. The condensation will seep through the mortar and you'll get staining inside and outside. In the old days this wasn't a problem because coal and labour were cheap and every house had maids running up and down stairs with buckets of coal, keeping all the fires burning all day every day to heat them so the flues remained permanently warm and dry. When you only light your stove in the evenings or at weekends you will be trying to heat up cold brickwork.
More modern houses will have a class1 flue made out of concentric clay rings like hula hoops, built inside the chimney breast. This is better because it will warm up more quickly and moisture will evaporate, can't penetrate and you'll get a good smooth column of rising hot gases, creating a nice strong vacuum at the bottom. If your house has an old-style brick flue or an especially wide flue, a liner is the answer but these are expensive. I'm afraid the stove "industry" is probably guilty of bamboozling quite a lot of their customers into having a liner fitted when it's not needed.
As before, your local chimney sweep is your friend here - keep him on side and ask him to fit the stove; he will do it with a rodding port in the stove pipe to make life easier for himself when cleaning.