Rear sprocket
 

Find a cog on your current 8-cog cluster that you feel comfortable riding continuously, without shifting. Use that size cog and chainring on your fixed gear build.

If you're thinking about converting your 8-speed to single speed, start by reading everything here: Sheldon Brown on Single Speed Conversions

If you're building a separate bike as a single speed and just want to know how many teeth to get on your cog, I'd say start with 18. Maybe more if you live somewhere hilly or plan on using a big chainring. Fewer if you're really strong and have a chainring smaller than 46 teeth.

You also need to clarify for yourself whether you mean single speed, or fixed. You used both expressions in the original post. The solutions to converting a geared bike are different. Which are you trying to achieve?

Single speed is one sprocket, but it has a freewheel, so you can coast.

Fixed gear means that the pedals are forced to turn all the time that the back wheel is turning.

There are pros and cons to each.

Always start with Sheldon Brown: https://www.sheldonbrown.com/singlespeed.html for singlespeeds

for fixed gear conversions, go here: https://www.sheldonbrown.com/fixedgear.html