There is a bit of difference between public and private sector finance, so choosing a route will depend on the sector you’d ultimately like to work in. Although if you’ve been working with public sector and would want to work with schools then it sounds like you’d want to go down the public sector route.
AAT is a good basic course to do. You may be able to miss some of the units depending on previous qualifications and experience. From there then maybe CIPFA? I guess it would depend on whether your interest would lie in Management or Financial accounts.
Lots of qualifications can be studied at distance or day release. Think I’d recommend the AAT as a starting point.