I would run Cat5e/6 to every room in the house and put a patch panel in the basement. You might not be able to foresee a need for it right now, but it beats having to wire up non-cabled rooms after the drywall's on.

Wifi is fine for activities that are not latency-sensitive (ie. web browsing), but can get terrible for things like simultaneous HD video streaming to 2-3 devices, or simultaneous gaming and streaming. So at bare minimum run cables to areas where you are likely to have consoles, desktops, streaming boxes and televisions.

If you plan on having things like networked thermostats, then it wouldn't be a bad idea to run cable to their locations, too. There are also plenty of wifi thermostats available, but personally I would rather not entrust environmental controls to something as changeable and easily breached as wifi.

Security is really up to you and your knowledge level. A moderately secure environment would have devices to protect the perimeter (one or possibly many layers of firewall) as well as the internal network and its services.

Some of us work with commercial grade IT systems; for us, segregating network traffic into VLANs, setting up an Active Directory domain, a RADIUS server for authentication, two-factor authentication with smartcards, Network Access Protection, and a network intrusion detection system, would be a piece of cake. Others would likely consider that overkill for a home environment.

Security can be as simple or as complex as you want to make it. Most consumer networks have nothing beyond a Wifi password and the WPA2 encryption scheme. Some have guest wifi networks that segregate guest traffic from the regular traffic (this is fine unless you have LAN parties and need internal machines to talk to guest machines). Some have that and an AD or Samba domain to manage file level access.

Use whatever level of security you are comfortable with managing yourself. It might not be Fort Knox, but for most cases, it doesn't have to be.