"which protocol would you select if there is only one network route to the remote network? "

EIGRP I think would be the better choice. IGRP is basically outdated and replaced by EIGRP. Useful if you cannot use EIGRP due to router limitations. EIGRP - Useful in Cisco-only networks of basically any size. EIGRP is often called a hybrid routing protocol that incorporates the best of the distance vector and link-state algorithms. EIGRP calculates the route metrics in a similar way as IGRP but uses a technique to improve the detail on metrics. EIGRP is an extremely robust and efficient protocol that suits nearly any need other than inter-organization routing.