Sawdust or other high carbon/low nitrogen materials do use nitrogen from the surrounding soils - several studies have found that this effect is greatest within ~10mm or so. Materials with high surface area relative to the mass can exacerbate this effect.

We use the largest chips mostly for walking paths and between our rows in the annual veggie gardens. When we find pockets of really fine chips in the pile, we’ll sift those and separate out the super fine material to use as potting mulch for the plants we pot up. The remaining chips are used in our compost piles or as bulk material for hugelkultur style raised gardens.

As far as species selection goes, there’s not much preference. I think a variety of species gives the widest array of nutrients as they break down, which will in turn support a wider array of plants and animals making use of them.