One of the great things about owning a classic bike is the discovery that you can both work on them relatively easily and make parts.
Working on a small lathe making a bush, for instance, can be very rewarding, especially for someone who has never worked with machinery before. Just polishing something in a lathe can make it look or fit that much better.
Ok, we cannot all turn up a new crank or mill a cylinder head to change the compression ratio, but there are many items on a classic bike that someone with basic training, and an eye for safety, can produce (check your local technical college for courses on machine tool).
For the home mechanic, a few small specialist tools are adequate, but if you intend to undertake an extensive renovation, machining capabilities will be required. However, lathes, mills and even pedestal drills are not cheap.
Luckily there is a compromise: a tri-machine: a combined lathe, drill and mill, all-in-one. Although somewhat limited in their capabilities (primarily in the size of components that will fit into them), they are, nonetheless, very capable and affordable machines, costing around $2000 in some cases.
Another alternative is to purchase a lathe with a milling attachment. However, this tends to be the more expensive route.
The least expensive approach is to buy a pedestal drill with a milling attachment and multi-directional vice. However, this machine will not be able to turn a component, and the milling capability will be very limited.
If finances and space permits, a separate mill, lathe and pedestal drill are the best options. Many of the major US wholesale companies carry a wide range of machine shop machines.