You will be an FO straight away. You will become an SFO after four years. Once you are flying on the line, no one will know you are an SSP unless you tell them. They may guess due to your lack of experience, but there is basically no difference between your job description and that of a DEP.
Your pay will go up considerably over the five years because you start off so much below a DEP's salary. (64%, 73%, 82%, 91%, 100% of a DEP's salary in each year over the 5 years).
I believe you are 'frozen' for 5 training years upon joining; cadets were and I am presuming it is the same for SSPs. You can still bid to change fleets, and if BA need you on your prefered fleet, they will move you, but you should presume that you will be doing the full 5 years, even though you might be lucky and move earlier.
Hope this helps.