ZenNMotion

A very cheap way to have a cyclocross capable bike is simply find an old 70's- 80's steel roadbike with the old centerpull brakes- mafac, universal and the like. These usually have a good bit of tire clearance in the back (don't get a high-end racer, get a sport or other mid-market level). Plus the centerpull brakes have excellent mud clearance, great stopping power and you don't need to worry about canti braze-ons. Keep the 42t chainwheel, take off the 52t for a single ring up front, keep the front derailleur on to prevent chain- drop, install a bar-end shifter, put on some cross tires and you're good to go. I raced an old Schwinn my first season like that, 35c tires and lots of extra clearance, could even install fenders under the brakes when it later became my commuter. Not a lightweight, but still lighter that some of the mtbs in the C races and faster too. You can also find hybrid frames that will work too. But add up the costs- if you really want to race cross, you'll eventually want a real cross bike. But the makeshift can be done with little money, you can see if you like mud, and it makes a great commuter/utility bike later on.