What are the benefits and drawbacks of different recumbent seat styles?
In short: There is no definite answer and there are better places to ask.

Having used two different mesh seats (both with a cushioned sit upon part and a mesh back) and one kind of hard seat, I feel I can give some advice. But as most is a case of availability and preference, I will not be able to give a definite answer.

When cycling you sweat and with your back on or against your seat (depending on how much upright you are) you want ventilation.
So your wooden seat is out unless you can introduce a ventilation layer or system.

Next your position on the bike is such that you have much less options to take your weight (as you would do on any bike where your pedals are below you) so your seat will have to work with whatever springs and shock absorbers you have on the bike.
The more absorbers you have, the less flex or cushioning you need in your seat.
On a bike with no spring or shock absorbing you need a seat that takes up all shocks, not a hard one. Cushions can work but are hardly anytime enough.

On all 'bents I have never needed anything to keep me in place. On the other hand, I prefer to be able to change position a bit so I can use different muscles or skin spots to avoid problems on longer rides, just like you may want to shift around on a horses saddle or an upright bike.

The ventilation and cushioning can be aided by the cushion you select.
Ventisit pads are one kind which I have often seen in use, but as far as I know they are not the only kind around.

While I love the stack exchange sites, I feel a question as important as this should be asked where a lot of recumbent riders come together, exchange information and are willing to help out others. Like the Bentridersonline forum.
Again, there are others, but this is one I know that works.

Added:
If your bike is more or less standard or you plan to repair it to standard, why not go for a seat that is standard for the bike or as near to it as you can get it?
The designers have experience with bikes and the design is proven.