i went to the bottom of my garden and grabbed the wood you see in my sig

as DrRob said aim for hardwood tree's they wont degrade or break down over time in the water, pop down to your local forrest or woods and have a look around, try and pick something that has been dead for year's so to speak, uprooted trees that have been down for years is a good start.
only thing i would suggest is put it into the bath and poor boiling hot water from a kettle over it this will remove any surface bugs or crap from the branch no need to soak it unless you willing to soak it for months

if it floats just get a rock or something heavy to tie it down with thats what i did as my wood did float, it still dose a little now but not as much and its been nearly 2 years now since i had mine definably de bark it i would say, that process can be very frustrating haha again i did mine in the bath and using a knife just be careful
tannins is a problem in my eyes, i hate them some people like them, but filterfloss in the filter or even better carbon will remove them, DONT replace the carbon every 2 weeks it will take out the tannins after years and years just wash it out every few weeks
hope this has been any bit helpful
good luck i personally think finding wood from your local area or nearby is great far better than wood from a shop