Imho, 31 December is the simplest and most convenient year-end date in practically all circumstances as it dovetails perfectly with P35, RCT35 and other calendar-based returns. It also circumvents the notoriously trickly commencement & cessation rules that can trigger double tax charges in certain circumstances.
31 January is a particularly bad year end date as it is in the middle of a VAT period and a P30 period, and can expose the business to the commencement/cessation trap as mentioned above.
As with most matters of this nature, professional advice at the outset is highly recommended.