What are the most important skills for a musician to develop?

There are a number of fundamental skills for a musician to master. Posture, listening and reading must be three of the most important. There are many other areas to consider but we will start by exploring these three areas.

Posture:

This is relevant from the very first guitar lesson.
Relax: Feeling tense never helps. You need do little more than move your fingers and you certainly do not need to tighten your arms, shoulders or back. This will make you tired, slow you down and ultimately lead to injury.
Sit well: A solid chair is essential, dining room chairs are ideal if you are tall enough. Adjustable piano stalls are also very good. Your right foot should rest flat on the floor. The seat of the chair should be reasonably flat to help with your balance. You are not going to use the back of the chair so a stool is fine.
Your back should be straight. Any twisting in the back will soon cause problems. Your shoulders should be level and relaxed, let them widen and drop. I am a big fan of The Alexander Technique, I started studying it to improve my posture when practising and to help with severe back pain which lead to headaches. It made me much more aware of my posture and actually lead to an unexpected improvement in my performance. 
Raise your left leg: A footstool is essential. Apparently the ideal height for the footstall is the height of your hand, but this is assuming that the chair is the correct height and the guitar is a suitable size. My students usually have the footstall higher than this.
There are a number of accessories which raise the guitar whilst allowing you to keep both feet on the floor. You can see the choices on the Guitar Notes website. Many people like these and find them comfortable. I have always felt detached from the guitar. I would not recommend them for beginners.
Guitar position: Your left leg will be straight in front of you, resting on the footstall. The guitar rests on your leg, with the head of the guitar level with your head. Your right leg will have to be out to your right side to fit the guitar between your legs, but the guitar is probably too large if your leg needs to be further than 45 degrees. The guitar strings will point towards your right knee. The guitar will be tucked in, close to your body, you will not be looking at the strings.
Hands: Your guitar and arms should be positioned correctly to ensure your wrists do not need to be bent. It is possible to play with your wrists at extreme angles, but it is not efficient and can lead to sprains and Carpel Tunnel problems. We will talk about hands and arms at the same time because arm position is so important in helping to find an efficient hand position.
Right Hand (RH): Pretend you are loosely holding a tennis ball in your RH. Your fingers will be curled, but not into a fist. It is important that you are relaxed and that you feel no tension in your hands. Touch your fingers against the strings, just over the edge of the hole in the guitar. Now let your arm rest on the top of the guitar, remember that your wrist is straight. You will find that your wrist is away from the front of the guitar, but not arched.
The contact between your arm and the top of the guitar is important because it ensures the guitar is secure and stops it falling on the floor. The guitar is now in contact with both your legs, your chest and your right forearm. You can use a non-slip mat to stop the guitar from moving if you are having trouble keeping it still. Here is a link to buy Non-Slip Matting.
Left Hand (LH): Curl your fingers, but not your thumb. It helps to think of claws. Rest your thumb on the back of the guitar neck. The centre line of the neck is a good starting place. Your fingertips will be curled enough to rest on the strings without being flat. Remember, you press with your fingertips, not the pads.
Your finger tips and the pad of your thumb are the only contact points with the guitar neck. Do not strangle the guitar neck, or allow it to rest in the palm of your hand. The LH does not support the guitar in any way.
Music stand: Correct use of a music stand will help with posture. Beginners should have the stand at chest or head height to help keep the back and neck straight. Performers should learn to play with the stand much lower so the audience can see (and therefore hear) the guitar body. The stand will then be tipped back enough to allow easy reading, it will be almost flat. It is important to keep your head and neck straight and just allow your chin to tip down to avoid back problems. A safer option is to memorise the piece and not use music when performing.
It has been suggested by a number of respected guitarists that you should position the stand close to the left hand so you can keep an eye on your hand position whilst reading the music. However, this position is not possible if you are sharing stands in an ensemble. It can also lead to a twisted posture. I recommend keeping the stand in front of you. 

Listening

It is important to be aware of your own playing. It is easy to fall into the habit of playing without actually listening to the sound you are making. If you do not listen, you will not know what needs to improve.
Listen to the sound of your guitar. Does it sound smooth and full or thin and scratchy? Does it buzz?

Record yourself. It is much easier to hear your playing and work out what needs to be improved.

Reading

Many guitarists can not read. They may be excellent at playing by ear, or have superb  improvising abilities, but they are really missing out if they can not read. 

Reading allows you to communicate. You can learn new pieces and techniques, you can write music for other musicians to read. Importantly, you do not have to rely on your memory to perform long pieces.

It is best to develop your reading during the earliest stages of learning an instrument. Learning to read can be frustrating if you have already developed your technical ability.
The best way to improve your sight reading is to read as much as possible. The music must not be too hard; you should not be constantly stopping to work notes out. The music can never be too easy; if it is new, it is worth reading.