As an American of Taiwanese descent, I have a preference for traditional Chinese characters. However, for ease of learning and for pragmatic reasons, I would suggest learning the simplified characters first.
The traditional characters are used only in Taiwan, Hong Kong, Macau, and the overseas Chinese diaspora. Knowing the traditional characters will also give you instant access to 99% of the Japanese kanji in current use. The simplified characters are used in China, Malaysia, and Singapore. However, just the sheer number of simplified Chinese characters argues for its use by a foreign learner of Chinese. China has a population of 1.35 billion, Taiwan and Hong Kong combined have approximately 30 million.
Simplified characters are also known as "simplified" exactly because the number of strokes per character has been reduced. This makes for easier learning for the non-native speaker.
Once you have learned the simplified system, you can then proceed to learn the traditional script, which in my opinion, is a much more beautiful writing system, and opens your world to thousands of years of Chinese history and literature (although with computer technology, you can easily switch between scripts in electronic media).
Example of a famous Chinese poem in traditional script:
月落烏啼霜滿天
江楓漁火對愁眠
姑蘇城外寒山寺
夜半鐘聲到客船
Same poem in simplified script
月落乌啼霜满天
江枫渔火对愁眠
姑苏城外寒山寺
夜半钟声到客船
In sum, once you have learned the simplified script, you can proceed relatively easily to the traditional script.