The sound produced by the guitar is largely influenced by the player himself. So it is definitely worth taking a closer look at the fretting and picking hand.
‣ Try to press down the strings as close to the fret wire as possible. This way you need less pressure to produce a buzz-free tone and avoid damaging your fret wire and fingers. Unfortunately this is not always as easy as it sounds, especially when playing chords.
‣ Pay attention to the length of your fingernails and the part of your fingers that you use to press down the strings. In theory, it would be ideal if your fingers were at a 90 degree angle to the fretboard. This way you could press down the strings without accidentally touching other strings. Of course, this is not possible due to physical limitations. So some compromises have to be made here.
‣ In the beginning it is really hard to get all the notes to sound clear when playing chords. This is especially true for chords like F major. There is only one piece of advice I can give you: Don't give up too soon. It takes a while to develop the necessary strength in your hand and fingers. This is perfectly normal and just requires a little patience.
‣ In addition, it is completely normal that your fingers hurt from fretting the strings. Over time, your fingertips will develop calluses and you can play for hours without even noticing.
‣ When it comes to picking strings, you have a variety of options:
Each of these options produces a distinctive tone. Picking with the bare flesh of your fingers has a softer, warmer tone. Picking with fingernails or picks produces a harder, brighter sound. In the beginning, picking with the bare flesh is certainly a good choice because it gives you more control over the strings. Once you have mastered the basics, it is of course a lot of fun to experiment with the mentioned options.
‣ Another very important and controversial question is which string to pick with which finger and how many fingers to use for picking. I would argue that most players use their thumb to pick the low (bass) strings and their fingers to pick the high (treble) strings. Some have a stricter style, using the thumb for the low E, A, and D strings, the index finger for the G string, the middle finger for the B string, and the ring finger for the high E string. Others have a less strict style and pick bass notes with their fingers and treble notes with their thumb when it's appropriate.
Also the number of fingers used for picking varies from guitarist to guitarist. Some guitarists use only their thumb and index finger (e.g. Merle Travis and Doc Watson). Others use their thumb, index and middle fingers (e.g. Mark Knopfler) and the third group of guitarists use their thumb, index, middle and ring fingers (e.g. Chet Atkins). In very rare cases you can also see guitarists using their pinky (e.g. Tommy Emmanuel).
If you're just starting out, a stricter approach is usually easier. This means picking the low E, A and D strings with your thumb, the G string with your index finger, the B string with your middle finger and the high E string with your ring finger. Over time, you will surely develop your own picking style.
‣ One last thing on picking strings: In the image below you can see that I am picking the low E-string with the side of my thumb. Also my fingertips hit the strings at a slight angle. This is the result of the hand position I described in my text about body posture and hand positioning and will help you when you try to get into more advanced fingerstyle techniques like slapping or picking with a thumb pick and/or finger picks.