If I were you I would measure the width of the hub against the rear dropouts of your bike to make sure they match first.
Because 8 speed freewheels are very rarely used, chance is your wheel was set up for a 5/6/7 speed freewheel. The implication is that if you screw an 8 speed freewheel (which is wider) on, various unfortunate phenomena, such as the drive-side locknut barely outside the freewheel leaving the freewheel fouling the frame, and/or the chain fouling the seat stay when on smallest sprocket may arise.
Since you have already got the wheel, we are where we are. If you don't know what speed the wheel was dished and set up for then you will have to do some guesstimation, and if you think it can take a 32mm wide cogset without the above issues then I would suggest you get e.g. a
7 speed 13-25 freewheel - it has the benefit of being narrower than an 8 while will index well enough with your 8 speed shifter once limit screws and cable tension have been adjusted (which most probably can't be avoided whichever freewheel you get anyway).