Bitcoin was introduced back in 2009 and since then, much investment and research have focused on it. Key topics such as system vulnerabilities or the economic implications of leveraging an electronic currency have been widely examined. Other investigations have centered in analyzing specific parts of the system. Specifically, some work has focused on one of the key entities of the system, namely the miners, their activity and profitability. We extend this line of work to include transaction fees chosen by clients by presenting a complete analysis of the transaction fees and the implications for both the users of the system and the miners. In order to do so, we define specific models for clients, miners and the underlying peer-to-peer network based on observations made after analyzing historical data. Given this information, we examine the problem of choosing fees to pay for issuing a transaction and the selection of transactions added to a block by miners. We conclude that current strategies should be refined to address the expected growth in use in order to protect the long term sustainability of the system.