Most hardwoods, including fruit woods will work fine as drift wood. Wood that has been in the water for a long time will not likely release any tannins. If you start with dry wood, that has been dead for a while it can sink quickly or slowly depending on the type. The nicest pieces generally come from the roots, and a piece that won't sink can be attached to apiece of slate with a brass or bronze screw and the slate buried in the substrate.
Wood should have any bark removed, and can be soaked in a bleach solution if it came from the water, or it can be boiled to sterilize. I power wash it sometimes.
Recently i prepare a couple of dead chunks of weeping mulberry, by power washing to remove the bark and than soaking in a tank with a few more power washes when it got scumming looking. It has been in a tank with fish for about 5 months now and hasn't leached any tannins. It took about a month to sink.