A smaller or low-cost carrier could be a useful complement to a CVN for the US, or a means for a smaller power to afford sea-based air power.
Here is how not to do it:
1 - Start with a ship that isn't really an aircraft carrier at all, because much of its internal volume comprises a dock, barracks, garage and infantry supply depot.
2 - Decide that what you need is a fighter with the operating empty weight of an F-15 and a price tag 60-70 per cent of an F-22. Better yet, one that can't do CAS until Block 4 or 5.
3 - Ignore the need for AEW, tanking, EA &c.
If the Marines were actually serious about doing expeditionary air power off 3,000-foot runways (can't go shorter because they need C-130 support) they'd look at JAS 39E. Then do an SCB-125-type job on a few amphibs and go with Sea Gripen.