flights

just keep checking...use a site like https://www.skyscanner.com/ to get price alerts.

"When would be the best time time to purchase tickets to get the cheapest tickest." - As soon as they become available.
Both Ryanair and Easyjet have prices that start cheap and go up as the date approaches. They never have "specials". It is very very rare for prices to go down (I have never seen it, but I have read reports it sometimes happens).

Easyjet is already selling Liverpool to Krakow, for 16th Jan 2018 the current price is £37.99 (plus cost for checked in bags).

Prices may vary considerably according to the day of the week. But, like the previous poster, I haven't noticed them go any direction except up as the time of departure approaches. Only exception, and not common, is a snap sale as a loss-leader to draw attention to a certain route.

When Ryanair and Easyjet were new, they would sometimes have last minute sales to fill planes. But they haven't been new for a long time, and now most of their planes are full long before the "last minute." So, their prices start out relatively cheap, then go up as the plane fills. They don't need "specials" to fill the seats anymore.

I agree with everyone else - for lowest fares, book as soon as you are sure of your plans.