Musicians tend to develop some pretty bad habits in the hours spent hunched over their instruments. Playing properly is hard enough without having to sit straight.
I'd love to be able to tell you that it doesn't matter, but an awareness of the proper body position is invaluable. Yoga, Alexander Technique, Tai Chi Chuan and other forms of body awareness can help too.
The bottom line is like your mother said, don't slouch. Whether you sit or stand to play, keep your back straight. Allow your shoulders to hang back and down and your chest to be open. Don't overdo the puffy chest look, just relax and imagine a cord attached to the top of the head drawing upward and another one from your tailbone drawing down.
Breathe as normal and check in with your breathing as often as necessary to make sure you're not holding your breath or grinding your teeth when you play (I kid you not!).
Holding The Drum
Sitting is usually easiest for beginners. Sit on the front edge of the chair and hold the drum between your legs. Using a strap or your legs to hold the drum in place, lean it away from you so that the bottom is open (air needs to move in and out to allow the notes to ring). Adjust the height so that the face is easily accessible to both hands - just above the height of your legs when sitting is good, too high or too low can restrict your playing. Give your elbows room to move and keep your back straight.
I've found it's easier to play with shoulder straps if you're standing. The drum should fall between your legs and the face should be around belt height. Keep your knees bent, back straight, head up and give your elbows room to move.
You will need a strap for this. More on straps below.
Sitting On The Drum
In more relaxed settings it may be easier to sit on the drum while it is lying down.
You'll be able to play fairly comfortably for a while, although this may not be the ideal position to play a long session.
Using A Strap
Option 1: The shoulder strap
Best for when playing standing. This requires about 2m of nylon or canvas belt.
The belt is tied onto the drums vertical ropes, making a large loop.
The loop is then passed over the head and shoulders to keep the drum in place.
It's a great system that provides a lot of room for movement and makes it easier to hold the drum standing up.
Make sure to adjust the length of the large loop to suit your size.
Option 2: The belt strap
Used for playing either sitting or standing. For this you will need a good strong strap with hook eye clips on either end. Take the strap around your waist and clip either end on to the lacing of the drum as shown. This should take all the strain out of holding the drum in place with your legs.
Now you're ready to move on to Lesson 2 - The Notation