In this paper, we propose an analytical framework for determining the outage probability of random and best relay selection schemes given a Poisson field of relay nodes and the presence of path loss and fading. For relay selection, relays geographically close to the source and destination are preferred to others. This selection guideline ensures a target quality of service (QoS) and reduces the signaling overhead and the relay selection delay. A spatial region called the QoS region is obtained for the random relay selection and is shown to shrink as the distance between the source and the destination increases and the interfering node density increases. When the QoS region for random relay selection is not large enough and cannot probabilistically ensure a reliable relay therein, the best relay selection is employed since the required relay node density and selection range for a desired QoS can be reduced for the best relay selection. The gain of the best relay selection with respect to the random relay selection is quantified in terms of relay node density reduction and coverage extension due to selection diversity.