Methanol (bp 64 oC) is not a trivial separation from the ethanol/water azeotrope (95% ethanol bp 78.2 oC). Complete separation would require a careful fractional distillation with an efficient distillation column. With careful monitoring of temperature the methanol would distill as a forerun. Other wise a larger volume forerun that contains both methanol and the azeotrope would need to be collected to separate the methanol from the bulk of the ethanol. In either case careful monitoring of temperature and distillation rate would be required as fractions of the forerun are collected.
Concerning the production of ethanol it is preferable to avoid making methanol, and start the fermentation with a pure cultured yeast geared for the brewing/production of ethanol, and known not to yield methanol. The yeast should be started in high concentration in a small volume so that many actively reproducing yeast are introduced to the bulk of the material to be fermented. In this way any competing organisms have little chance to compete with the rapidly dividing "brewers yeast".
I am fond of brewing my own hard cider as it requires little effort in comparison to beer/ale. I start with freshly pressed cider, or cider that has been pastuerized or UV treated. Don't use cider with preservatives (potassium sorbate) as it will inhibit any fermentation.
A portion/cupful of cider is warmed to ~ 35 oC/95 oF, added yeast nutrient (a dead yeast) and yeast energizer (diammoniom phosphate and urea) , a packet of brewing yeast (all from from brewing supply outlets), then lightly capped in a jar in a warm dark place. Fermentation will begin and I vent the cap often to allow carbon dioxide to escape and relieve pressure. The bulk of the cider is allowed to warm overnight as the starter is actively fermenting.
A 5-gal carboy is cleaned and sterilized with soapy bleach, well rinsed, and equipped with an air lock. To the bulk of the cider yeast nutrient and energizer is also added then transfered to the carboy. Cider alone will generally ferment to ~ 5-7% ABV ethanol. Additional sugar may be dissolved in the bulk of the cider (sugar, brown sugar, honey) to increase the amount of alcohol produced in the ferment. If a large amount of sugar is added a yeast must be selected that tolerates high alcohol concentrations, or the yeast will get "drunk" and fermentation will stop yielding a very sweet cider. If all the sugar gets consumed the cider will be very "dry" like a dry wine.
I like a good strong cider and add ~ 1-lb of sugar/gallon, and use yeasts made to brew champagne or strong wines that can approach 20% ABV (Lalvin EC-1118 or Red Star Pastuer Champagne). The starter and the cider with the above amendments (enigizer nutrient sugar) added to the carboy, the airlock secured, and the batch allowed to ferment in a warm (75-85 oF) dark place. Don't add more than 4-gal to the carboy as considerable foaming will occur. If this get out of control the carboy can be placed in a bathtub of cold water until the fermentation subsides. The ferment is then monitored by the bubbles of CO2 observed leaving the airlock. When the bubbling stops either all the sugar is consumed (dry hard cider) or the yeast is drunk (sweet hard cider). The mixture will be very cloudy with considerable must/wort/yeast forming a layer on the bottom.
At his point I allow the yeast to settle and cider clear. Some people will "rack"/transfer by siphon the partially clear ferment into a 2nd carboy to finish the settling process. I am just patient and wait until the cider clears. The longer you wait the clearer it gets, plan on several weeks-month. You can still bottle partially cloudy cider and the remaining yeast will settle in the bottles. This sediment will get disturbed when pouring out the contents, but just results in a cloudy last glass full with care full pouring.
I bottle my cider into 750-mL bottles with re-useable caps, or 1/2-gal beer bottles. Smaller bottles are a PITA to clean. They should be clean/sterile and the cider is siphoned into them. It is handy to have a siphon made for this that brewing suppliers sell, it has a device on the end to avoid siphoning the must from the bottom of the carboy. If the cider is dry, a
small amount of sugar can be added to each bottle to get a 2nd ferment and a sparking cider. Only use bottles designed to take pressure and don't add too much sugar. If one bottle bursts, it sets off a chain reaction.......
I won't get into distillation to make the real hard stuff. A good friend makes wine and distills that to make grappa. I've been doing orgainic chemistry for a long time and have distilled lots of things besides booze.