The long term benefits of being publicly traded are numerous and can include: improved liquidity, higher company value, the ability to make acquisitions or attract and retain employees with the newly public companies stock and greater access to capital at a lower cost.
In addition, having public trading status allows a company the ability to make acquisitions with their stock, since publicly traded stock is viewed as currency for mergers and acquisitions. More over, public trading status often leads to a higher price for a later offering of a companies securities.
There are many market places you may consider to go public in the world, however, in the USA, even a Small Business still can go public.
There are four main ways a company can "Go Public" in the USA.