I was in a really similar situation to you, my dss was 3 when my and my dp got together, i was only 22 and now nearly 6 years on, things are still going strong.
My advice would be to take things slowly, and that in time, things will become a lot easier and you will find the situation quite natural. The advantage of the child being so young is that they dont really understand the situation and will naturally be more accepting of you. I began by building my relationship with my dss accompanying them on days out, or watching family films etc where there is no need to be anything other than someone they can have fun with - id say that this early on in your relationship (both with your dp and dsc) there is no need for you play any role other than this. Are you living together? We didnt live together for the first 3 years of our relationship, and for the first 18 months, i didnt stay over whilst dss was staying at his dads, just to make sure i was introduced to their dynamic gradually. I think this had a lot to do with us being younger though so it might not be practical in all relationships.
When you talk about discipline, what sort of things do you mean? In my experience, most "naughty" things that three year olds do, arent intentionally naughty, but just because of their age (e.g. tipping their toys everywhere etc). I always took it that if dss was in my care, or even both of our care, it was fine for me to gently discipline/guide him, e.g. "dont do that its dangerous/you will make a mess" etc or encouraging him to say please or thank you - i dont think anyone would find it unreasonable for you to say these sorts of things, as long as you didnt start shouting at or getting angry with him. Also my dss always understood that i was an adult and if i asked him to do something, he would just do it because at that age they dont know any different, an advantage of them being little, and i think if you establish this from the start you will be ok. If dss ever did anything really intentionally naughty, which was rare, i would show my disapproval but leave the decision over discipline to his dad, even if it meant waiting for him to get home. However as he has got older and i have been in his life longer, we have started to show more of a united front over any really naughty behaviour, and if my dss did anything really naughty, my dp would support me in disciplining him (e.g. taking a toy away or whatever) because we want to avoid him playing us off, and because we want his time with him to be as close to normal family life as possible.
I found that treating dss as my own when he was with us helped me to develop a good relationship. Some people might disagree with this, but when he stayed with us or we took him on holidays, he was a little boy away from his mummy, so i wanted to look after him as a mummy would. I took on that role of dressing him, sometimes bathing him, reading him a story, putting him to bed, making him food, cuddling him, playing with him, taking an interest in his school work, sometimes looking after him on my own or taking him out if his daddy was busy (all gradually in time of course). I didnt want to take the attitude of leaving all of his care to his dad when he stayed over, because i felt it would create a divide and make it seem like i wasnt interested in him.
We intentionally acted as though we were a "real" family when we were together. He came on all our holidays with us from the start, and if we got invited to any family friendly events (parties, weddings etc) even by my friends and family, he came with us, even if it was on a day we wouldnt normally have him. It has really stood us in good stead now that we have recently had a baby together.
I would just go with the flow for now, but your dp sounds like a good dad and im sure he would be more than happy for you to develop a close relationship with his child because he will want him to be apart of your family unit. Any discipline issues or family decisions come part and parcel of this. You sound really caring and taking a considered approach to stepparenthood so without meaning to sound patronising, im sure youll do a great job :-)