I think putting together logistical support for the men and their horses (feed, blacksmiths for shoes, etc) there would be a ratio of 3 followers to each soldier. There is no factual or statistical basis for this number but this is also Game of Thrones, not the Westeros version of Risk. A baggage train of 800-1200 would perfectly acceptable, and in that there are going to be cooks, craftsmen, retainers and entourage for leadership, prostitutes, animal handlers, and general followers on. Being that this is a Lannister venture and they aren't poor, there could likely be a large number of beggars and followers looking to survive off the largesse of the unit.