What you have to also understand, while your fame does marginally increase from doing repeatable quests, some quests rely on "triggers" from other ones.
For instance, a few quests in Sandoria cannot be received if you haven't finished certain other ones revolving around it, not even necessarily by the same person.
Thus, I would recommend finishing as many of the easier quests as you can. Your fame will rise quickly enough.
Fame is instaneous, it doesn't take time to "tally up" or anything like that. :)