Congratulations on being a first time mom. My first bit of advice is that this is not going to be easy or smooth sailing. All babies are different, all babies will be wonderful one day and the next turn into a different child! But no worries, you are his mom and you know best, and what works for me or someone else won't work for you necessarily. However, each of us will probably suggest a technique, but overall you have to learn to watch your baby and learn his own quirks and go from there.
Ok with all that...here goes my advice.
Babies will sleep varying amounts during the day and night. "Sleeping through the night" according to the APA (American Pediatric Association) is 5 straight hours at night. You however have to help your child between feedings and a consistent routine will help stretch the time out and gradually he'll start sleeping in longer intervals. I'll start out by saying my daughter didn't sleep "through the night" (8 hours) until she was 8 months old, my son was about 5 months old. Probably b/c I knew what I was doing with him and not so much with my daughter.
Go buy or check out from the library The No Cry Sleep Solution by Elizabeth Pantley, an AMAZING book which helped us and will help you learn some easy, simple, "duh huh" thoughts about sleep! At first a baby will sleep more because they are growing and need their rest. During your daily routine, make sure you feed your baby (breastmilk or formula) and try to interact more and more with him. He'll want to sleep and usually will fall asleep at the breast or the bottle but he'll gradually grow out of that, but the soothing comfort is very nice for newborns. Make sure you play and use toys for him to grasp or work on his gross motor skills or his tracking skills with his eyes, or soft books to chew on or look at. READ to your child, even if they are sleepy and not into the idea of reading, listening to you and to the words is key!!!
Try to work on keeping him awake more during the day and start with a consistent night time routine. You choose what works for you, but I did this with my son when was about 8 weeks or so and have not change it a bit. We didn't do this right away with my daughter so it took a bit longer. But we head upstairs around 7:30 or so depending on your child and how long of a nap and how long he's been awake, you judge, but we go up and we either bathe or get ready for bed. During the winter months we bathe just about every other day. Only b/c the weather makes everyone have really dry skin, and they don't get that dirty during the day anyway. So we just head up and either get a bathe or get dressed. Read books, clean up our toys, keep things and activities in a calm manner, nothing to exciting. And they know it's time for bed. We snuggle, sing, and have one on one time with them and put them to bed with a quick kiss and we leave. Yes, we LEAVE the room. In the beginning he'll probably cry, and want you back, but I usually don't make eye contact and I leave the room. They both know it's bed time and they both roll over and go to sleep and they sleep through the night.
There will be times when they won't d/t to bad dreams, teeth, wet diaper, a cold, you name it but you just need to remain calm and trust yourself to put them back to sleep. DO read that book, it's well worth the time and money if you buy it. Read it now while he's still young and you'll learn what to look for.
All of what you said, sounds perfectly normal to me. Just enjoy them while they are young. It only seems like yesterday I was bringing her home. Sigh...take care.
A. B