Summary

Selective permeability comes from hydrophobic interior of nuclear membrane since phospholipids have fatty acid tails which are non polar
Small non polar molecules (N_2,O_2,CO_2) pass through freely
Small non charged polar molecules (H_2O,NH_3) can slip through in small amounts
Ions and and large polar molecules can't cross and require channels or transport proteins.
Cell walls in bacteria, archaea, fungi and plants provides structure, protects against osmotic lysis and acts as a permeability layer for some substances.

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Cell wall material:

Bacteria - peptidoglycan
Archaea - various polymers (not peptidoglycan)
Fungi - chitin
Plants - cellulose Cell walls maintain shape and mechanical strength, permeability layer, protection from osmotic lysis (rupture via influx of water).