The most common question I got is which Chinese language to learn?

Short answer: Mandarin.

Long answer: China has a large territory. There are 56 ethnic nationalities and each speaks their own language, for example, people in Hong Kong speaks Cantonese (their local language) in addition to Mandarin. The largest ethnic group is Han which consists more than 90% of the population. The national language is mandarin (普通话 pǔ tōng huà). Mandarin is the formal language or the national language of China. Everywhere in China, people should understand it.

TIP: One thing that China expats would find it useful is to know, at least, a bit of chinese.

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What’s the best way to learn Chinese?

Of course come to China and learn it there. But say you can’t do that... First, do some research. Ask what kind of Chinese they are teaching. Many of Chinese classes taught in the USA (or available via web sites) are not Mandarin -also books in libraries. (I came to China with one quarter of non-standard Mandarin Chinese in college.) There are Taiwanese, Cantonese (widely spoken in Hong Kong for example), Singaporean among others. They are not Mandarin. The dialect is different, the pronounciation is different (although some is pretty close) and of course the way to write. Chinese language is evolving as people move in and out mainland China for thousands of years. For example 中国 and 中國. Both are the pinyin of Zhōng guó, means China. 中国 is the standard Mandarin or also known as the simplified Chinese. Other examples: 门 vs  門 (mén, door), 妈 vs  媽 (mā, mother), etc. Also notice, if you go to local China town, don’t be surprised if many don't understand Mandarin or you can't recognize some chinese characters.

Some online schools whose teachers are from China are not bad. I know these folks: MasterChinese, you could give their free trial class a try. I think, they try hard to deliver their best and they have good scholarship/programs for native english speakers. In China, there are many good schools too to learn Chinese. I went to BLCU since it's close from home :) They are good but they only accept full time students. To learn Chinese online probably is not a bad idea, really.

Should one work hard to master the four tones?

Mandarin Chinese has four tones which you can read about extensively elsewhere or here. If you want to really master the language, I encourage you to practice really hard at it. Ask your tutor to teach you intensively how to pronounce the four tones for all types of possible combinations. We spent a few weeks doing this intensively every day in my class. It's really important to pronounce things in correct tones if you want others to understand you. Many characters have the same pinyin but different tones. For example: mā means mother but mǎ means horse. To put it bluntly, it's close to useless if one can't pronounce words with correct tones.

What if my native language is blah blah?

It doesn't matter. My classmates came from all over the world: France, Costa Rica, Mexico, Russia, Thailand, ...  You name it. The rule is, just like to learn other languages, study hard and you'll master better. Some might argue a Japanese should find it easier to learn Chinese since some of the characters are the same. True, but that gives only a slight advantage in the beginning. Ultimately, those who study hard (review characters daily, write daily, do homework, etc.) will prevail. Practice! Try to speak, listen and be active in Chinese conversation to accelerate your progress. After a while, you can start hearing sounds, see patterns and start to try to imitate how native speakers speak or write.