I am a ham radio operator, and I have read a lot on grounding and antennas, and I have my setup heavily grounded with 8 ground rods, a radial system, blocks, etc., so I will try to keep it simple and not give bad info (some of this is reiteration of what was already posted):
1. You want all grounds to be at the same potential - the one serving the house and the one serving the antenna - this means they need to be connected together (bonded), and best done outside.
2. You can get zapped or your electronics zapped by lightning just near by (miles even). Enough voltage can be induced in your wiring to cause a discharge. I have been shocked on my electric fence once after I pulled the plug but touched the wire during a flash. The voltage came from the lightning two miles away induced in the fence wire! So it isn't just a direct hit you are working with - and the nonsense that your tree is bigger and will be hit first is crazy! Induced voltage (EMP) is more of an issue frying your electronics, and that doesn't need a direct hit to be trouble for you.
3. You want to get the voltage to ground outside, not through your equipment or in your house. A good grounding block should be ideally outside, and directly below the mast, Drive a ground rod there. Connect this rod back to the service ground of the house using thick (#6 or #8 solid copper) wire. Wire can be buried. Connect another grounding block before the entrance to the house and ground there as well. What you are doing is trying to direct the lightning/voltage to disappate where you want, not where it wants. If it hit the antenna, it will likely go straight to ground there, if it is induced, the long cable run is now the pickup of the voltage which is why you want to ground it directly outside before it comes in your house.
It isn't the easiest topic, and there are consequences for getting it wrong - But a good system doesn't have to be expensive, but it does have to be installed correctly. I have seen profesionals run their grounds with nice bends and turns. Lightning doesn't zig-zag, it usually goes fairly straight. Good ground wiring is rarely pretty!
The other major thing is having the grounds bonded together. If you don't, the path of least resistance maybe through your house and wiring! When everything rises and falls together, the strike's path of least resistance to ground is outside - where you want it! If your entrance is all the way on the other side of the house, most professionals will tell you to run a cable all the way to the other side of the house - some even will say put a ground rod every 16' along the way.
There is more to it, of course, but these three principles will help most people still reading this thread.