Firstly, I think it is great that you are considering nursing your second child.I think too many people just do the same with the second as the first and that is not always what is best.
I wholeheartedly wanted to nurse my children for what I felt was the nutritional benefit, though I was very uncertain about what nursing would entail and how I would possibly do it in public.
I nursed both of my children, a son and then a daughter, and they nursed in entirely different ways. My son had a hard time figuring out how to latch on (suck properly). For the 1st 24 hours after he was born I had numerous nurses and lactation consultants in the room, each offering their own bit of wisdom to help my son get the hang of it. I was quite exposed, and I was surprised that it didn't bother me at all. I'm not suer if it was because I felt I had just bared all to give birth, or because I felt so strongly about doing it for my son, but I wasn't self-conscious in the least. I think that was important. I was very open to their advice and critique and tried my best to stay focused. After trying to get him to nurse every 2 hours around the clock, he finally caught on and from then on it was perfect :o) My son ate very frequently for the first few months of his life. He would nurse just about every 2 hours, night and day, and I was quite tired. After 3 months or so he nursed 5 times a day, so it was easy to schedule outings and what not. My son weaned himself around15 months old.
As for nursing in public, I honestly never imagined that would be something that I would do. When I first came home from the hospital, I even went upstairs to nurse, rather than do so in front of my MIL. With time, I got over it. I never once encountered even a scornful glance from a person while nursing. I was very discreet, and I never had a nursing cover. I realized how incognito I was, when on two separate occasions, my husband's uncles approached me to talk to my son, not realizing I was nursing until I told them! I never planned my day around needing to nurse. If we were at a park, I could just find a private bench to do so. If we at a friend's house, I would either private go to the couch or use another room. At home, I always nursed in my living room, no matter who was here. I always gave advanced notice to those present so they could choose to leave the room if they wanted, however.
My son loved to nurse and it soothed him. He would remain at the breast for 30 minutes to nurse, and would often fall asleep there. I had feared that weaning him would be difficult, but it was simple. He was ready, and he just stopped.
My daughter was entirely different. She literally began nursing when only a few minutes old. She caught on instantly. She was a power nurser, only nursing for 10 minutes at most. She was not comforted by nursing, but rather saw it as a mode to gain food :o) She did weigh slightly more than my son at birth (my son was 8lbs2oz, she was 9lbs) and I am not sure if that is why or not, but she never nursed as often as my son did. Even from teh very beginning, she never got up more than twice in the night to nurse, and she would typically go at least 3 hours during the day between feedings.
With my second, I had my husband more involved. I am a stay-at-home mom, so with my first, I felt it was my job to do it all. Remembering my exhausting with my son, we decided that in order for me to be at my best with two kids, my husband would get up in the night to help with my daughter. He simply got up, retrieved her from her bassinet, changed her diaper, and delivered her to me in bed, where I nursed her. When she was done, I'd whack him and he would put her right back. My husband has a much easier time going back to sleep than I, so he didn't mind at all. It was so much easier on me too, because I wasn't nearly as awake since I stayed in bed the whole time. I wasn't even tired with my second and nursing was a breeze. She also weaned herself around 15 months.
Well, I am sorry that this turned out to be so long. I just want you to be able to make an informed decision about something that I feel very passionately. The bond that you form with your nursing child is instant and amazing. I never saw it as a burden or something to be embarrassed about. I wish you the best!