If you're desperately
needing syncing across multiple devices (honestly, it doesn't take that much effort to scroll to the last tweet you read -- I follow nearly 300 people and all I do in the morning is grab my phone, scroll down to the last tweet I saw before going to bed, and scroll up from there), Echofon will do the job -- it syncs across platforms. Free for ad-supported, I think it's $4.99 for ad-free.
For the best desktop
client, I'd say it's TweetDeck (which is free, and now owned by Twitter).
I wouldn't spend money on any 3rd-party clients right now, though. Twitter has just instituted another tightening of its regulations for its API, which indicates another crackdown on third-party clients. Major third parties like HootSuite will likely still continue to have an API license, but Twitter's ecosystem is looking at a bit of an upheaval in the very near future. Tweetbot, Echofon, etc. -- Lord only knows where they'll be in two or three months.