MadMango is right - it's very dependant on the manufacturing route taken before the bar stock gets to you.
The above mentioned standards will give you tables of machining allowances and dimensional tolerance on the diameter of bar stock, but these are very generous and in a commercial manufacturing environment are sometimes considered uneconomic.
You need to consider other variables - what size is the production run? How critical is the 2.5" OD and over what length? It might be more economical to purchase preturned or preground barstock and let your vendor make the decision on what original hot rolled size they use.
One component a previous employer manufactured was induction hardened pins for mining applications. When I got quotes for material from vendors I would stipulate something like 'material to finish dia 2.5" h9 X 400mm length. QTY 500'. With eddy current crack detection as our final step we could ensure conformance. We saw a wide range of material size and eventually found trusted suppliers that sourced their material from excellent mills. In my experience steels from Imatra, Ovako, Corus, Ascometal, Ronane, Mitsui, Nippon have excellent cleanup. (sorry, very limited exposure to US steel). You'll find cheaper material but it is a hit and miss affair.
In the above example, it was a medium size run in a competitive manufacturing environment. It was important for us to have the raw bar stock as close to the finish diameter while giving acceptable rejects. If the job was one-off and no crack detection was available, I would have played it safe and used 70mm or 75mm bar stock.
There we are - a very long way of saying 'it depends'.
Lew