My experience as a recent father: remember every baby and so are the experiences are unique. We had welcomed a beautiful angel five months back.
For the first couple of months, if you have elders who can support, it would be really helpful (we didn't have any, still were able to pull it off pretty well). In the first month, she slept really well; we had to struggle to wake her up for feedings. Occasionally, there were sleepless nights with the baby crying, making you feel like consulting a doctor since we would have no idea what's happening and making you worry like hell. Over time, we understood it's common and it's usually problems with digestion/growth spurts/sudden changes in their development, but if possible, have a doctor who can be available on the phone for the initial months; they'd usually say it's normal, but it's better to have one.
Follow only the doctor's advice for the mother's diet and baby care. Some of the elders/relatives/friends' advice may not be necessary and should be avoided, like pressing on the soft spot on the head, dhoopam treatment for the head (not sure what to call it really 😄), etc.
For sleep, try to follow the same pattern every day and make the baby sleep in the same environment and setting. That has helped us to a lot of extent after 2 months. We bath her with warm water mostly in the evenings, which helps with her better sleep. We made sure to follow the same routine every day, which seemed to have worked for us pretty well, and she slept through the night; we only had to wake her up for feedings.
Regular tummy time helped in faster neck strength, after which you feel pretty confident in holding her. Do read about the wonder weeks, which will help you prepare for the baby's milestones and what you can do to help them grow and reach developmental milestones. (1/2)