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 damage to 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 with which you 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 make all the notes 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 before you have developed the necessary strength in your hand and fingers. This is perfectly normal and only requires some patience.
‣ In addition, it is completely normal that your fingers hurt from fretting the strings. Over time, your fingertips will form 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 master the basics, it is of course a lot of fun to experiment with the mentioned options.
‣ Another very important question that is controversially discussed is what 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 in a stricter way: the thumb is designated to the low E, A and D string, the index finger to the G string, the middle finger to the B string and the ring finger to 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 differs between guitarists. Some guitarist only use their thumb and index finger (e.g. Merle Travis and Doc Watson). Others use their thumb, index and middle finger (e.g. Mark Knopfler) and the third group of guitarists use their thumb, index, middle and ring finger (e.g. Chet Atkins). In very rare cases you can see guitarists also using their pinky (e.g. Tommy Emmanuel).
If you're just starting out, a stricter approach is usually easier. That means picking the low E, A and D string 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 style of picking.
‣ One last thing on picking strings: In the picture below you can see that I pick 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.