How would you keep america safe while creating a unified force?

I would consider models that have been based on the British system; as exemplified by the Canadians, Aussies, Kiwis, and the South Africans.

As MAJ Balligner pointed out, centralized functions that exist within all branches should be combined and attached to the force which it is most alligned with. Air Movement would obviously need to be an Air Force function, whereas some more land based and port-based logistics operations should remain in the Army. The Naval force would maintain it's seaborne focus. This would open up the opportunity for "joint" type assignments (look at JCSE as an example) which could open up career advancement and broadening that does not exist under the current branch system. Think of how servicemembers in functional jobs could move across forces to get new experiences and work for promotions. A servicemember in supply could spend one tour in an Army Infantry unit, then get assigned to a ship the next tour since supply functions could be standardized across services. This could permit for a dramatic variety for many servicemembers which could make their careers much more rewarding.

I think the trick then comes with what standards are utilized. I frankly think that something that lies between the Army and Navy as far as typical standards would work for a baseline. The standards would have to be able to hold a wide-variety of personnel accountable to maintaining the standard; which is why something as strict and confining as the USMC would likely not work across an entire military. Traditions could still be maintained, and taught at a unit level. The naval force could maintain the seafaring traditions but the ownership would be less on force-level traditions and be pushed into unit-maintained traditions which would likely be based on the previous traditions already established.

Given, just the baseline development of an idea would be enough to drive several PhD candidates research projects for decades. The combination of branches would take a lot of work and each service would be lobbying in the DoD to maintain their identity and to have the most influence.

I do bet that we could find a way to have a much more powerful, well-trained, larger force through this due to the fact that the budget could be streamlined a bit and some of the fat could be trimmed in the process.

The whole idea is a Pentagon nightmare. Someone with too much time on their hands. Downsize, but remember the creation of the best military the world has ever seen was not done as a unified force. It was accomplished by competition, pride, and manufacturers whom vie for the contracts. R and D is the order of the day. Combining will remove almost all the R & D that takes place between the branches and limit us to just a few companies who win a contract and thus can survive over the long term. Imagine for one minute the construction of a ship and the production of a airframe being managed by the same people. Who would that be? Who is currently qualified to do that? The Aussies have an experience infrastructure that goes back in layers for generations. We would be destroying the best for the opportunity to become immediately one of the most inexperienced and worse managerial mistakes in history.