I don't think much of tweet-deck. Maybe it's because it uses Adobe Aero and who wants to install any more software than necessary and let's face it: Twitter is still pretty useless...
I do however get "twats" to my Android phone, using both Twitgit and Twidroid. I will comment on the later some other day, cause it's really well developed and free.
But I found a widget for the Google Homepage that works fantastic and keeps you up to date with the twats you receive - it's intriguingly called 'TwitterGadget' and looks something like this: