You need to find yourself a good book on transformer design or do a good search of the web. Stick ferrite is not particulary good for transformers - I would suggest an E core or toroid for this application. You could get something from an old PC power supply, but the actual specs for the core material you would have to guess. The thickness of the wire is usually determined by resistive loss - the number of turns is governed by the volt turns required (use transformer calcs), so you can estimate what your require.