For some traders, they will only trade a selected currency pair such as EURUSD. By specializing, they feel that they can understand the currency pair better, hence they will trade better. The decision is up to you.
As for me, I will look at 20 over currency pairs and see which currency pair presents me an opportunity. By looking across all currency pairs, more opportunities present itself and it gives me a better feel of the market, hence i can usually identify the strongest and weakest currency. I will buy the strongest and sell the weakest currency, thereby choosing the best pair to trade and catching a strong trend.
There is no right or wrong answer to this question. Basically, you trade whichever currency pairs you like. As a rule of thumb, trade the major currency pairs such as EURUSD, AUDUSD, GBPUSD, USDCAD and USDJPY... By trading the major currency pairs, there will be more liquidity in the market, you will enjoy lower spreads, there will be more volatility and more opportunities present itself.