How do you use Twitter in OS X?

How do you use Twitter in OS X?
Iʻve set my OS X System Preferences / Internet Accounts to have my current account.
When I use Twitter in Safari, I get "VIEW [thousands] of new tweets", and it dynamically updates. Terrible to use.
Itʻs annoying because sometimes I want to have music play from the Mac, and not have VoiceOver talk over it (I know, I need to get a BT headset to hear VO just "in my head").
Or is there a better way? Some other app?

Forum: 

#1 Easy Chirp

I've been using Easy Chirp ever since I got my Mac, and even before that. It is web-based, and works great both on Windows and Mac OS. The website is http://www.easychirp.com . I haven't tried out any of the Mac-based Twitter clients, but perhaps I will someday. But what I like about Easy Chirp is that it is free, and totally accessible. The lead developer is Dennis Lembree, and he is very responsive. He recently teamed up with another guy.

#2 night owl

Night owl works well and it can be found in the app store.