There is no such thing as the 'true' sound of an electric guitar. You've described three valid methods of recording yours.
Direct connection plus Garageband effects gives a pleasing result? Good.
A cheap microphone that looks designed to flatter close-miced vocals was less successful. OK. Maybe it overloaded. Maybe you should point it at a different ...
Option 2 is the traditional way and would still be considered the “proper” one by many engineers. Obviously though, the Frontman isn't exactly a boutique amp, so you shouldn't be surprised if this doesn't give results that are as good as what you hear on professional records. To go the amp route you should
Have an amp whose sound you really like. Typically ...
All 3 at once.
Mic'd amp because you know how it sounds and what you record is what you get
DI'd signal so you have something to re-amp if you don't like #1
GT-6 because why not?
Then at mix time you can work with a blend of the 3 to achieve whatever you want.