You should probably use the old road bike for a couple of your first cross races just to make sure you like it before you invest in a new cycloross bike. You can get tires that will fit in your frame; Vittoria makes a really narrow cross tire. As far as shoes go, regular mountain bike shoes are fine but look for some that have a little flex in the toe (for running) and have some kind of buckle closure system (Velcro and water don’t mix). Sidi makes some of the best shoes for cross but there are other less expensive models as well.