心掛ける is a good one to learn.
毎日Xをするように心掛けている。
I'm working hard at doing X everyday.
Also, 努める or 努力する
毎日Xをするように努める(努力する)
If you overly use 頑張る, it sounds strange, especially when you use it for things like "reading a newspaper". You should use it for something more "important" like studying for a test or trying to get a job or something.