We'll I was just about to shamelessly plug the 3 part article on my blog (below) about setting up a home network, both wired and wireless....but my hosting company appears to be having issues.

Edited to add:
Links are back up.... home network guide, Part 1 Part 2 and Part 3

I favor a mixture of the two media. But if budget, time and a lack of willingness to put holes in your walls are issues then go with Redburgundy's suggestion. Try wireless first.
I'm a little unclear how directv plays into the mix, other than that if you are running coax you might as well pull cat 5 too. However, if you need wired network access, say for regular (non-directv, or hacked dtv tivos) then wireless bridges (devices that receive the wireless signal and then give you a jack to 'hard wire' into) can get expensive quickly.

Another thing to consider is what kind of traffic you'll have. If you plan to move videos around then hard wired is the way to go. Even if you dont have gigabite ethernet, the 100mbs speed that Ethernet provides blows wireless out of the water. 802.11g touts 54mbs, but its fairly rare to get that kind of speed and any sustained rate.

In terms of security, you are absolutely right, wireless can be made quite secure. However, that takes a little effort to set it up correctly. I fall into the paranoid category around here, but I feel strong about this. The only kind of security that is effective for wireless is WPA/WPA2 with a very long, random passphrase. I recommend the full 64 bit sting that WPA supports. Check out www.grc.com/pass for a site that will generate strings. Then copy the string to a $20 128mb USB thumb drive. When you need to setup new devices on the wireless network, plug in the drive and copy and paste. To be clear ssid hiding and mac filtering are not security but means to obfuscate your network. WEP is older security and can be compromised by a 13 year old and a $100 laptop off ebay.