You will sit in this for more hours than you sleep in your bed. Of everything in a workspace, the chair is where the money is best spent. Here is how the types differ.
Mesh
A mesh back flexes with you and lets air through, which matters if you run warm or work somewhere without air conditioning. Mesh chairs tend to look more like office equipment and less like furniture, which is a real consideration if the chair sits in your living space. Good mesh is supportive. Cheap mesh sags and stops supporting anything within a year.
Leather
Warmer to sit in and considerably better looking in a room that is not an office. Leather executive chairs usually have more padding and a higher back, which suits longer periods of sitting still. They run hotter, and a full leather chair in a sunny room in August is a genuine downside.
Fabric and linen
The middle ground. Breathes better than leather, looks softer than mesh, and disappears into a domestic room more easily than either. Harder to wipe clean, so think about it if you eat at your desk.
What actually matters more than material
Seat height adjustment is non negotiable. Your feet should sit flat on the floor with your thighs roughly parallel to it. If your feet dangle, the chair is too high and the front edge of the seat will press into the back of your legs all day.
Lumbar support matters next. It should meet the inward curve of your lower back rather than the middle of your spine. Adjustable lumbar is worth paying for, because backs are not standardised.
Armrests should let your shoulders drop. If you are shrugging to reach them, they are too high and you will feel it in your neck.
A note on recline
A chair that reclines and holds position lets you change posture through the day, which is the same argument as a standing desk and just as valid. A chair locked upright encourages you to sit in exactly one position for hours.
Castors
Standard castors are made for carpet. On hard floors they roll fast and can mark the surface. If you have wood or tile, either buy a chair mat or swap the castors for soft rubber ones, which is a five minute job and cheap.