March 25th would be a good new year as it is (I think) Spring equinox. I also guess though that while Spring equinox now lies around then, in the dim and distant past when there was much confusion about how many days, weeks, months etc. were in the calender it could have fell on April 1st.

If anyone knows how and when the days were added, deducted, jugled or otherwise cocked-up it could well explain what used to happen when!

Cheers

D the G