I've just bought a project recumbent. It has no seat yet. There are many different types - why would I choose a mesh one over a solid one?
Mesh style - a HPVelotechnik "ergomesh"
"Bench" style - a HPVelotechnik "bodylink seat"
This same shape comes in metal or wood as well as carbon fibre.
an AAZZAA brand seat
A homemade carbon fibre seat
A homemade steamed and laminated plywood seat.
Edit: In the end I was lucky enough to find a used M5 seat for sale, was a lot easier than making my own. Since then I've acquired a complete HP bent, so no need to make one. Both seats are in the shape of the wooden one pictured, and are made of fibre-reinforced plastic with a topper pad for comfort.
The main takeaway from my time on both seats is that ventilation and the ski-jump are critical, while the head support is relatively low importance.
Lack of Ventilation means that after a commute I end up with a puddle of sweat in the small of my back, soaking into my clothes. Dressing lightly to the point of being cold helps some, but its unavoidable.
The ski-jump is the lip/crest at the bottom of the seat, the foremost part. Picture #2 and #3 have quite a lip up, whereas the HP seat I have now has a curve down, which is horrible and feels like you're sitting on a wire, and sliding down. Perhaps my back-side is a poor fit, so I ended up padding it with pool noodle around the front which helps.
Basically if you're large, a mesh seat would work better. If you're small/thin then a narrow solid seat would be fine. For touring/all day rides get a mesh seat. For going fast, a narrow solid seat.