Honestly, I can never remember what “group 1″ and “group 2″ refer to, but regardless, the way that works best for you is the way you should learn it.
Ichidan and godan are the Japanese names for the groups.
Ichidan verbs, sometimes called る-verbs, have a single verb stem that remains unchanged however it’s conjugated – they’re called る-verbs because the plain form stem always ends in る, and you conjugate by dropping the る from the end. For example 食べる -> 食べます、食べない、食べた、食べられる. This is what Koichi calls “Group 2″.
Godan verbs, sometimes called う-verbs, conjugate by changing the verb stem itself – they’re called う-verbs because the vowel on the end of the stem is what gets changed. For example: 飲む -> 飲みます、飲まない、飲んだ、飲める and so forth. This is what Koichi calls “Group 1″.
Confusingly, some godan verbs can end with る as well. This is part of the issue with defining the verb groups in Japanese – however you phrase it, there’s always going to be exceptions, verbs that look like they belong in one group but actually conjugate like the other.
The reason Koichi describes “group 1″ verbs as ending in い is because in ます-form, the godan verb stem always end with い. But again, there’s exceptions – some group 2 verbs also have verb stems that end in い anyway, regardless of how they’re conjugated. Like すぎます or みます. Koichi talks about that on this page.