As a military veteran (I was an MI officer in the US army), I would have to agree with many of the previous posts. Yes, military rank structure has been looooooong established, and perhaps trying to invent new ranks for a military that is comprised of people descended from Earth origins may simply be creating smeeps all over the place--you know, calling a rabbit a smeep just because. People are generally familiar with sergeants and captains, etc., so you would not have to spend precious word count and tedious explanations explaining it to the reader--or worse, leaving them floundering while they try to figure it out sans explanation. More importantly, the structure works, and works very well, to the point that law enforcement often emulates military ranks. "Captain" is so long established from naval warfare stretching back thousands of years that I have a hard time especially envisioning that rank ever going away.
That said, if you are going to do it, remember that function drives the structure of your military force. You may simply have "leaders" and "fighters" with no other ranks, or you may have a very elaborate structure based on what the various units are actually doing. In the US army you have squad and even section leaders for very small unit functions. Specialized teams may need one guy in charge of 1 or 2 others and he has a specific rank. There may be 50 of those teams within a standard unit and the "commander" might simply be the most senior of the squad leaders. He may never see most of his guys from day to day because they are scattered in areas of operation far removed from headquarters. You might even have elected leaders as in the US army up to the Civil War when militia companies were raised in support of the regular army. On your world, Old Joe might actually have some ordinary civilian title, in that case.
In my current WIP, I have a squad structure called a decim (10 guys), commanded by a decimark. The company or troop is a "hundred" commanded by a captain (still thinking about that term) and the "army" of about 10 hundreds is commanded by a First Captain. You could have First Sword for that matter, or anything else that designates him as the top-ranking guy. Just think about
how your people are fighting and how they're organized to do it. I wonder how small, dispersed terrorist operations are structured and what the head guy is called. They are certainly cohesive and operationally organized without the usual military ranks employed at all.
The mission of your military at every level of conflict will determine how it is organized for ground/sea/air/space operations, and that includes command of the logistical bases required to support it. Those guys might have an entirely separate set of ranks for staff/support folks as opposed to combat troops. The US army tried that for awhile with technical ranks that were not supposed to hold authority over troops but eventually pretty much did away with it except for warrant officers, who generally have pretty specialized knowledge.
At any rate, the structure of command means just that: everyone has a way to recognize the authority of everyone else in relation to their own. This means that job descriptions are not a good way to do this, because two mission specialists doing completely different, specialized jobs still need to know who gives the orders if everyone else gets killed. It can't just depend on "I've been around longer than you." Date of rank is always the tie-breaker, but it also, to some degree, indicates that Sergeant A has some degree more experience than Sergeant B. Mayhem may result if B has no combat experience and A does and they're in a combat situation, but one hopes B has brains enough to turn over command in the interest of saving his own skin.
Good luck, and have fun with it!