I like the big two-volume Chinese English dictionary from (I think) Shanghai Jiaotong. There is also a Taiwan edition. I also think the De Francis ABC Chinese-English Dictionary looks like it would be useful though I don’t own a copy myself.A somewhat more eclectic recommendation is Pulleyblank’s Lexicon of Reconstructed Pronunciation in Early Middle Chinese, Late Middle Chinese, and Early Mandarin. It’s very, very useful for getting handle on classical usages. These pop up more than some might think in modern written Chinese.
Best of all, all three are ordered in Hanyu pinyin!
Here’s a tip: if you are studying in Taiwan, you should never have to look up a word by radical. Just swallow your pride and ask someone how to read it. Then you can look it up in your Pinyin-sorted dictionary. This is also where Zhuyin fuhao comes in handy. Even though your Taiwanese friends may not hit every retroflexed zhi, chi, and shi, they will almost certainly know how to spell it out correctly in Zhuyin Fuhao. Looking up characters by radical is a huge waste of time (You should make an effort to learn the radicals, but that’s another story).
This is an under-appreciated part of learning Mandarin in Taiwan. Everyone in Taiwan under the age of 45 seems to know Zhuyin fuhao well. I find that people’s grasp of pinyin in China varies widely.
I think that one should start using a Chinese-Chinese dictionary as soon as possible. I started off with the Guoyu Ribao dictionaries and later moved on to Guoyu Huoyong Cidian from Wunan publishing. This one still sits on my desk. Chinese-English dictionaries are dated and (often) misleading, especially in Taiwan, where usage has diverged considerably from that in China. As Ironlady has mentioned before, Google is probably your best bet for many new terms.
Of course, any serious Sinologist will want a copy of the “Daluban” Ciyuan published by Taiwan Shangwu and, eventually, the Hanyu Dacidian in 12 volumes (make sure you get the last volume with the pinyin index!)