Hi there.
I have just started in the civilian Airline industry from being in the Military. From what I have found out, speaking to engineers. You need to have your own basic mechanics tool kit. There are lists on several websites. A friend of mine got me a list from Airmech.com. I managed to cobble together a selection of tools from that. I can only speak from a Military viewpoint, which buys there own tools. However from what I have been hearing, rumour wise, is that airlines are starting to invest more in getting thier own tooling as it reduces the risk of FOD and unregisterd tools getting lost. The amount of money you have to pay for your first tool kit varies, depending on what brands you buy. I go for Snap On, as they have a lifetime garentee on them. They are expensive but look on e-bay. I managed to get hold of a load of good Snap On tools from a retired engineer for a bargain. I don't know if you can charge a fee from your airline, for replacment tools though. I don't think you can, though I could be wrong.