Honestly, since your goals are so open ended, you can train pretty much however you want here and you'll be fine. If you trained using only dumbbells, you'd get bigger and stronger. If you trained only using barbells, you'd get bigger and stronger. Barbells for 6 months dumbbells for another? Same. Barbells 1 month, dumbbells only for your right side 1 month, dumbbells only for your left side 1 month...weird, but bigger and stronger by the end of it no question.
When you start chasing more specific goals, you need more specific approaches. If your goal was a 225lb strict press, I'd suggest spending more time with the barbell at first, developing mastery of the movement, and then maybe spend some time with dumbbells to bring up weak points.
All THAT being said, your above comment about how performing more than 9 sets for a bodypart in a week leads to decline leads me to believe that you should honestly dedicate some training time to improving your conditioning. It sounds like your recovery might be a little lacking, and this could be holding back your progression. Some conditioning followed by a super high volume block might do you good.