Ideally, you want to get as little of that sediment (trub) in your keg as possible. That can be done by cold crashing or even by simply letting your fermenter sit for a few days before kegging. Some people cut the diptube (what you call a straw) but I prefer not to, so I get all the bout. You'll get sediment for the first glass or 2, but after that you'll be fine.