1. A vehicle position estimation system to estimate a position of a vehicle using an image captured by an image capturing device mounted to the vehicle, the vehicle position estimation system comprising: a device configured to be mounted to the vehicle; and a server that is connected to the device via a network, wherein the server comprises: a first wireless communication device configured to communicate over the network; a first storage medium that stores landmark information for a plurality of landmarks, the landmark information including, for each landmark, a respective subject recognition range that represents a respective distance range of the landmark, a respective landmark image of the landmark, and a respective recognition evaluation value that represents ease of recognition processing using the respective landmark image; a first processing unit programmed to: calculate, for each landmark, the respective landmark image by averaging a plurality of previous images of the respective landmark; and transmit the landmark information to the device with the first wireless communication device via the network, and wherein the device comprises: a second wireless communication device configured to communicate over the network; a second storage medium that stores the landmark information received from the server; and a second processing unit that programmed to: receive captured image information corresponding to the image captured by the image capturing device mounted to the vehicle; execute landmark information selection processing in which the landmark information to be used in the recognition processing is selected from the landmark information stored in the second storage medium based on the recognition evaluation values of the landmarks in the landmark information stored in the second storage medium which have the subject recognition ranges that correspond to a first position of the vehicle; execute the recognition processing in which a characteristic object represented in the captured image information is recognized as one of the landmarks from the landmark images of the selected landmark information stored in the second storage medium; execute position estimation processing in which the first position of the vehicle is corrected to a second position of the vehicle using the landmark information corresponding to the recognized one of the landmarks; and transmit a landmark evaluation result message including a recognition result of the position estimation processing to the server with the second wireless communication device via the network, wherein the first processing unit is further programmed to: execute update processing in which the recognition evaluation value of the recognized one of the landmarks of the landmark information in the first storage medium is changed based on the recognition result of the position estimation processing included in the landmark evaluation result message received from the device.