Dear Engineers,
Without going into any in-depth design I have just checked roughly the steel column size required for the stability concern, i-e, the size required to keep the slenderness ratio (k l/r) within 200, it comes out to be around 36 X 36 inches X 1/2 inch thickness, which gives the slenderness ratio of 187. I am not sure about the thickness requirement at this stage because it will also be governed by the fulfillment of strength requirements, i-e, the design load-moment interaction. I believe that every code has the stability requirements (The slenderness limitation), depending upon the importance of the compression member itself, it may sometimes be less than 100 in some codes, better to check with the code upon which the design is being carried out. I took the height of column as 150 feet and assume "k" as 1.5, which may increase depends upon the boundary conditions at column top. I suggest that a truss type of column be selected and also to keep in mind the workability / Installation process while designing these columns.
Wish you good luck