You will need a lathe and a milling machine with the usual tooling items. You will need a horizontal/vertical rotary table for your mill if you want to duplicate the visual design aspects of some of the projects - spoked flywheels, fluted columns etc., but the engines will operate just as well without those features.
If you are using small equipment, most of my projects can be scaled down to suit - but remember that as engines get smaller, they are usually harder to build and don't run as well as larger ones. If you intend to only build small models that can be held in one hand (more or less), then table top machines with the proper accessory items will be just fine for you and will save you money. All things considered, if you do not have your machine tools yet, try to acquire machines with greater capacity than the projects you intend to build with them and of the highest quality you can afford. Also remember there is absolutely NO SUBSTITUTE for mass in a machine tool because it will dampen vibration and chatter.
I am often asked what equipment I use to make my projects. I use a 1968 Maximat-7 (7 inch) lathe, a 1990 Maximat Super 11 ( 11 inch) lathe and two Jet JVM-836 (8x36) knee mills, one of which I converted to CNC in January 2007. Click here if you would like to see them. The Maximat lathes by Emco-Maier had been out of production for a number of years, but sometimes one will come up for sale on eBay.