The best uses for birch as far as I have found are;
Tops: besom brooms and hurdles (horse jumping).
Long straight trunks: 6" dia or smaller can be cleaved into 4 or 8 down the length. Check quality. Straight with no twist makes good longbows. Any with a twist, trim roundish and make yurt khana (walls). Shorter straight pieces can make milking stool legs or other rustic furniture.
Burls: Cut these out and keep for bowls, knife scales etc.
Branches: Look out for interesting bends that'll make good spoons and set aside.
All the rest: Chainsaw up and make charcoal. That includes all the non usable twisted or gnarled bits, all the waste and anything that can't be made into something 'value added'.
The advantage of making charcoal is the saving in weight. It sells for four times as much as firewood given the same amount of raw material. It's easy to do and a great way of clearing up felled timber. You can also mix other hardwoods with the birch for charcoal. You don't need a metal kiln (about £700) to start with, a couple of 55gal oil drums will do just as well. Another advantage in charcoal is you don't need to season the wood as long. Typically a year for firewood (ash being the exception) but you can have a charcoal burn of birch in just a month or two after cutting. I've even known burners use it green just to get them started.
Eric