To get started, you should have accurate job descriptions for your existing staff and develop an organizational plan -- including projected hiring dates -- for the future. Often, putting together a series of organization charts, for example, by quarter is helpful in planning out your company's future growth.
As you have already identified the three ladders, you should develop job descriptions for the job families that will come into being as you continue to expand your staff.
Job families in large companies might look like: Scientist I (being the entry level job); Scientist II (requiring more education/experience/training); and Scientist III (being the most senior individual contributor job in this family reserved for the most expert.
Just as with top management, there should be very few at the extremely senior level in any job family. The same kind of levels with job families can be used -- albeit with titles appropriate to the roles -- for the administrative and management arenas.
Of course, as your company is not a large one, you can be more creative with the titles while still following the theme of a junior employee, a journeyman and a most senior level in each job family. And, there is nothing to preclude having more than three levels, if you need these.
Management of your career ladders will require that you adopt a sound job evaluation system that links to a salary grade chart so that you are paying properly for each position -- not only now, but as people progress within the same job and receive merit increases to their base pay or bonuses for their contributions and/or are promoted to higher levels in the organization.
You should work with a compensation expert to help you construct your plans. Your employees will feel more confident knowing that you took the extra time and expense to do this in a meticulous manner.
Related: How to Hire With Fit in Mind
Related: Seven Ways to Boost Employee Morale