Use a natural firelighter or paper and sticks with your all natural lump wood charcoal. You can cook directly on the charcoal once white by avoiding using any petroleum. It will also avoid any nasty taint of flavour affecting your product.
Prepare your charcoal on one side of the BBQ enabling a two-zone cooking area. This is great for steaks and most product as you have a hotter and cooler area.
Once your BBQ is hot, use a decent wire brush, and scrape your grill to clean. This will clean it far better than trying to wash it.
Generally, it is good practice to slowly cook on a BBQ and then finish on high heat to create a lovely texture.
You can find many ways to cook over fire via the internet however.