There are two kinds of ranks: officer ranks and enlisted ranks. In order to achieve any rank, you have to invest the correct number of points in the trait "rank". The more points in rank you purchase, the higher your rank. In addition, if it is an officer rank, you have to also purchase the trait "commission" to reflect that you are now a commissioned officer and have attended Officer Candidate School.
Lieutenant is usually the lowest or second-lowest ranking officer, so usually it is sufficient to purchase commission and 1 or 2 points of rank to become an officer. Sergeant is a non-commissioned rank, so you do not need to purchase commission. You will have to purchase, on average, about 6 points in rank to achieve the rank of sergeant. Further, each military has a slightly different ranking structure, so how many points it requires depends on the army you're going into: 1 point of rank + commission makes you the equivalent of a lieutenant in the Draconis Combine Mustered Soldiery (they call them Chu-i's), but in the Armed Forces of the Federated Suns, it requires 2 points of rank + commission to make the rank of leftenant.
