Can I use a cyclocross bike for regular road-biking purposes? I want to race cyclocross, and I also want to ride some longer rides out on the road. Can I buy a cyclocross bike and use it for both cyclocross and some serious road rides (I'm talking century type rides)? Or will I be uncomfortable riding long rides on a cyclocross bike?
You can absolutely ride road on a cx bike. Many of the components are actually road components, including the wheels, so slap a pair of 700x23's on the stock wheelset and off you go.
Things to consider: 1)Cross bikes are going to be a little heavier than a road bike in the same price range- probably a couple to a few pounds. Ultimately not that big of a deal if you're not riding road competitively. 2)Some may argue, but it's ok to be wrong... cantilever brakes are inferior to road calipers, at least on the road. I wont get into why cx bikes use cantis as there are plenty of explanations across the interwebs, but you won't get the same control out of a pair of cantis (or v's/mini-v's) that you'll get from road brakes. There's a reason that they're different. The best substitute, and they're getting much easier to get your hands on now since discs recently became UCI legal for cx, is frame/fork combo built to accept disc brake calipers. Again, they're slightly heavier than canti's or v's, but the overall feel is worth it, both on and off the road (and especially in the mud!)
3)This is probably the biggest one in my opinion...
Though they are similar, ultimately the feel between a road bike and a cx bike is noticeably different. Among more subtle differences, Cx bikes have longer wheelbases, higher bottom brackets, longer chainstays, and slacker headtube angles than road bikes do. These are all good things when riding off the road and in the mud because they lend to the bike's stability. On the road however, these geometry differences translate into a slower steering, more sluggish feeling bike. Once again, there's a reason that they're different.

That said, my cx bike probably sees the same amount of mileage as my road bike does. I ride it on the road regularly even for longer rides and it is a great commuter. If you need one bike to do it all and you don't plan on hitting seriously gnarly mtb trails (they can handle light to moderate singletrack duty), a cx bike is the most versatile machine you can own.
To answer the next part of your question, you 99.99% of the time you are going to come out on top financially by purchasing a complete bike as opposed to piecing it together by buying parts separately. Building a bike from scratch is fun and you get exactly the build out that you want, but in my experience with many bikes it has never once been cheaper
Finally, to find the right bike, go to several of the reputable bike shops around you and try out what they have. Due to geometry differences you may like one bike better than the next or one may fit you better than the rest. Test rides are key. There are a ton of great bike brands out there and a lot of your choice may come down to personal preference. Find a shop with a good fitter. Bike fit is important for all styles of bikes, but it's crucial if you're going to be spending a bunch of time on the road. Some shops will throw a professional fitting in with the purchase of a new bike. Be sure to ask. 
Good luck!