AVG used to be good, not so anymore.
As a fully qualified Microsoft certified systems administrator, I can tell you your requirements for security depend on many factors. Expertise, what will you be surfing, do you open emails from people you don't know, do you only accept txt emails, etc etc.
If you are unsure about computers then yes get it secured up, but beware, AV companies often build their latest software based on latest hardware, if your system is old it could seriously slow down.
Spyware and malwsre, rootkits etc are your real enemies when it comes to security, personal details etc etc
Just to add, a common option if you are worried about viruses is.
Download latest avast
Install
Update virus sigs
Do a full scan
Leave PC for a few hours
Check results
If all ok
Uninstall.
If problems found address them and keep it installed.