You may first need to find out what is available to you in your area. In alpine areas of Europe variations on the softwood theme are frequently all that is available, so chimneys are built accordingly and people cope. Timber to burn will rarely justify the cost of moving it very far from the source.

I knew someone years ago who burned teak for several years having bought up old parquet floors when some substantial local buildings were demolished (they wouldn't get sold off for a song these days) He reckoned it a first class fuel, and ready-cut into handy pieces too, but these days I would expect folks to recycle it as flooring.

Fruitwoods from grubbed-out orchards are a possibility in some areas, and nicely aromatic if you can obtain them, but most well dried hardwoods are OK. Avoiding elm is a sound policy, it smokes and stinks.