Reducing sound output from a typical bedroom can be extraordinarily difficult. The core problem is that sound travels through the point of least resistance -- you can get a good sound block in one area, but find it makes no difference since the sound just escapes from somewhere else.
If you have a hollow core door, then that is one of your biggest sound holes as a typical hollow core door has an STC rating of only 20 or so. That's not going to do a lot for any noise above a whisper. But wait, even that is not a true representation of the actual sound transmission. The problem is that rating assumes we are only talking about the door and not the air gaps around it. If you have a hollow core door, then I'm going to assume that it's not properly gasketed. If so, then the actual STC rating is substantially less.
Can you make that door more sound absorbent? No, not really. At least not in any efficient (money and time) manner. Your best bet would be to upgrade to a solid core door. If you have a standard door, then there is a good chance that the hinges will even line up and it'll be a straight swap for maybe $100.
Doing so will immediately jump your sound blocking to an STC rating of 25 or so. Eh? That doesn't sound much better than a hollow core door! Well, that rating is taking the air gaps into account, so it's actually substantially better.
But STC 25 is still not going to be good enough to make a big enough difference in your sound transmission. To do that, you're going to need to control the air gaps. If you add some acoustic door gaskets, then you'll be looking at an STC rating of 35 or so. That's actually quite good -- roughly on par with the STC rating of your wall. People will still be able to hear what happens in the room, but it'll be notably muted.
An alternate to buying an interior solid core door and adding acoustic door gaskets is to buy an exterior door, which is already going to be solid core and will have its own seal. That could be expensive, though, and the hinges will almost surely not line up.
If it is a split jamb it will not matter it will gauge itself to the wall thickness. If it is not, and you have an older home with 3 5/8" studs circa 1950-60's with 1/2 sheetrock, you will need the wider jamb. If it is a newer home, you may be able to go with the narrower jamb.
The biggest downside to a smaller jamb, is there may be a gap that can occur at the point where the trim meets the jamb. It can be caulked is it happens. This is still unlikely though since the trim has a relief to allow it to bridge over some unevenness in the assembly.
The biggest downside of the wider jamb is the reverse, a gap at the wall to the trim, but it will only happen at the corners, unless you force it back, which will then open the joint.
I would go with the wider jamb without seeing the conditions, if the walls are out of plumb a little you can use the extra width to tweak the jamb into plumb without going too far behind the face of the wall on either of the four corners. If the wall is too far out, use a plane to get the jamb edge closer to the wall face can be done too.
Best Answer
Warp is a very important point to consider. Though depending on the species and the cut, this answer could very a lot.
Pine may be lighter, but also has a much higher moisture content. If the door is kiln dried and sealed quickly, you can keep it from absorbing the moisture from the humid air. Also if it is air-dried, it may be more stable. I have seen pine warp significantly due to changes in humidity, and being in India -- especially if you are in the South or East -- I would wonder if this wouldn't be the case as well. (especially if it was a knotty pine)
Hardwoods are denser, and generally have a lower moisture content allowing them to dry well and remain more stable lowering the chance for major warp.
My opinion: Go hardwood.