Actually most people seem to play those games in third person, while The first person perspective is one of the things I totally enjoy in these games. I usually play my way through the main quest and then start working on all those side quests which is when both oblivion and skyrim really shine. There is so much to find and see and so many different shorter and longer stories.
I also really enjoyed the crazy world of oblivions shivering isles addon as well as the feeling of seeing the updated morrowind architectures in skyrims dragonborn addon, which isn't perfect but added some pretty cool new settings and quests.
I btw didn't enjoy oblivion for quite some time until I just played it for a couple of days nearly nonstop exploring different guilds and quests and everything.

As you error, I too do enjoy linear games with a strong story usually the most, which is why my absolute favorite games are heavy rain, Fahrenheit and penumbra, but Lately I also liked far cry 3 a lot, just focussing on the story.