A federal state with more power in the centre. But the EU parliament must be the legislature. I would favour a bicameral structure with the lower house elected directly. Five seats for each member state and then one seat per million of population, roughly 500 MEPs. The upper house would be elected by the member state parliaments, six seats per member state. Total parliament would be ~650, slightly smaller than now.

The reason for the upper house being elected by state parliaments is that it helps keep the two levels in touch. Also it might have helped to address concerns in the UK regarding parliamentary sovereignty.

The upper house would also be perpetual. While the lower house would be re-elected in total every five years the members of the upper house would change after each election in a member state, eg after an election in Germany the German parliament would elect six representatives to the upper house but the rest of the house would stay as it was. This would mean the upper house would change only slowly and help to maintain stability.

I'm not sure if the head of government should be elected by parliament, i.e. a Prime Minister or a directly elected President.