I feel compelled to disagree wrt the tones. In spite of the fact that my tones are decent now, they weren't during the early years of my China endeavor and I didn't miss out on too many beats.

My Advice:

1) The more context you provide, the better. For example, I still have problems pronouncing "投资" properly, but never encounter any confusion if I use it in a sentence.

2) When in doubt, default to first tone. There are actually Chinese people that speak in this manner ("farmer Chinese"), and it works for them

3) Many foreigners mistakenly confuse tones with pronunciation. In other words, they mistakenly blame their horrible Chinese on tones. With the possible exception of "r" words, Mandarin sounds are really easy for westerners to pronounce.

4) Don't take the, "Chinese is a hard language to master," bait; 25% of the global population speaks it and the majority of them are no smarter than you guys.

5) Building on the last point (in part because I'm loath to post a 4-item list), it's mostly subject-verb-object, and many words can serve 3+ parts of speech. What this means is that a bit of rote memorization can take you a long way.