It should be a tree (or a network with as many reticulations or fewer, compared to the number of reticulations you will ask for your network search) with the same taxon labels as in your data. I think it should not have polytomies (it should be binary: fully resolved). This topology is what the search will start with. The search will modify this topology to try and find other topologies that fit your data better. Over and over, it will modify the best topology found so far, to try other topologies and improve the fit to the data.
In theory, yes you can use any gene tree to start the search, so long as it's fully resolved. But a consensus tree (fully resolved) should be better, because it should fit the overall data better. The advantage to choosing a starting tree that fits the data well is that it should speed up your search: if starting from a good point, so the search should end sooner than if you start the search with a random and poorly fitting tree.
I hope it makes sense.
C.