About purifying ethanol - What type of ethanol?
Forget about the denatured alcohol! Additives are typically chosen to render their removal difficult. 

Supposed you have decent setup for distillation, analytics still might be a problem. 

How will you determine whether your destillation was successful or whether it just was "thermal transfer" from one flask to another?

A hydrometer to measure the density of the liquid could be helpful. 

Use some cheap vodka, mix with water and try to distill the vodka off. Measure the density before and after distillation. Note the temperatures, read about strange things that can happen: azeotropes. Cheers!

If you want it more simple and obvious, mix the vodka with some food colourant. Proceed as before and watch the effect. Cheers again.

Note that one usually would not digest anything that went through any lab equipment  for mixed used at a normal lab. But this is your home lab and you know what went through which labware. Anyway, keep your equipment clean and take care. Btw: Cheers!