The Welsh Lib Dems, who share power in four council areas but control none, have pledged to cut all school classes to a maximum of 25. At present they are 30 or fewer for infants and should be the same for most Welsh junior pupils by September.
Mike German, local government spokesman, said: "We believe that smaller class sizes benefit both teachers and pupils."
Other policies include a three-year funding guarantee to end uncertainty over school budgets, and protection for closure-threatened small schools.
The Lib Dems are also committed to access to Welsh medium education.
The Welsh Tories, who run Vale of Glamorgan without an overall majority, want to reduce government bureaucracy. Good schools would be allowed to expand, and parents given more choice over which school their children attend. The party also opposes village and church school closures.
David Davies, the party's Welsh Assembly education spokesman, said:
"Teachers will be freed from unnecessary interference and red tape. This will include a slimmed-down national curriculum and the scrapping of arbitrary government targets."
Plaid Cymru's local government manifesto focuses on a new needs-led funding formula for schools, and better provision for early years and childcare, particularly in deprived areas. The Party of Wales will want to hold on to Rhondda Cynon Taf and Caerphilly, the Labour strongholds it won at the last elections five years ago, in addition to Gwynedd.
Janet Ryder, the party's education shadow minister at the Welsh Assembly, said: "Plaid Cymru believes in an integrated, inclusive education system from early years to university."
Labour is going into the local elections on its education record, claiming standards have risen along with the numbers of teachers in schools. Its manifesto flags up national policies such as free nursery places for three-year-olds and the Sure Start programme for early years.
Locally, Swansea councillors are highlighting their success in providing broadband internet access in schools, while in Wrexham the Labour authority has reintroduced grants for uniforms as well as providing American-style yellow schoolbuses.
For the European elections, Wales counts as a single constituency with four seats. Ten parties have candidates, including the British National Party, the UK Independence Party, and the left-leaning Forward Wales - whose four-strong slate includes former Welsh secretary Ron Davies.