Let me cover the two concerns one at a time.
i agree wired connection is the secure way, if you turn off wireless. period.
however, you can expect reasonable security with wireless if you follow standard recommendations like mentioned below. please not that these are just examples not a complete list. (unless you see a construction van is outside your home for a few days
1. change the default passwords of router and modems . can't stress enough. more than 95% of hacking can be stopped by this.
2. for extra security, only allow known devices by mac address. you can do this by visiting routers admin console.
3. do not open ports on router, keep it as factory default.
4. always keep firmware updated.
5. following email attachment opening & phishing guidelines.
6. use any reputed firewall and antivirus software. free ones from microsoft are equally good.
7. don't open up file and printer sharing at home pcs. keep it simple.
the cable company usually sends lower grade ethernet cable in package. buy cat 6 cable, pretty cheap in amazon, use that to connect modem to router and any of the pcs at home. you will see noticeably difference. i even noticed my wireless streaming got faster.