Yes, your stepdad's concern is very reasonable.
See many threads in this forum relating to security measures which will prevent almost all but determined professionals from gaining access.
As your DELL laptop is new, it most probably supports WPA-PSK encryption (maybe even WPA2-PSK) of all data traffic received and sent by your laptop.
Match the wireless router you get, to also be able to encrypt with WPA-PSK or WPA-PSK & WPA2-PSK (AES).
Check that the router allows you to set MAC address filtering just to permit access for your wireless devices alone.
Personally, I would also disable the router's SSID broadcast so your network is "stealth cloaked", as well as disabling your router's "Ping" responses to automated probes.
The router would also probably have a firewall capability (NAT), which actually adds hardware security
~ you probably only have software firewall setup on your home BB-connected PC ~ the s/w firewall (with a few tweaks) added to the router's hardware firewall will increase your security layers.
It still would not be as secure as a wired-only network with a router though, but probably more then sufficient for home use.
You can always move more sensitive data into an obscure partition (which is not shared on the network of course), as well as encrypt it separately as well.