As for how to approach the games, I have had the same question, I have tried 3 times to playthrough Oblivion and have never progressed through the story, it took 3 tries on Skyrim and I literally had to force myself to play through the story missions just so I could say that I had.
I can tell you some things that I did that I don't recommend, but since I am not a huge fan of the games, (Only played Oblivion and Skyrim) my ideas are probably wrong. In fact I was accused on this forum of playing the game "wrong" which kinda made me realize Skyrim wasn't a game for me.
Anyway, I usually try to complete everything in a game in one play through. While I haven't changed this, one of my friends who loves Bethesda's games recommends otherwise, when we both got New Vegas on launch day, he beat the game 3 times before I beat it once since he loves to play thru multiple times.
With the TES, since there are multiple character layouts, you kinda need to play through the game multiple times to experience everything, I tried to go through the game and check off each skill one by one but when you max out one style of combat, all the other ones become useless, so I recommend mixing combat all the time OR saving magic or melee/bow for different plays.
Also, similar to my completionism, I try to evoke all dialogue options and get every bit of information from the game, which means it takes me hours to get through a single quest, I don't recommend this either. A large amount of the dialogue that isn't from essential people (quest givers) is basically a waste of time. Play through the game first, if you like all the back story, you can play through it again to get better insight, trying to learn everything will make you hate the game and will cause you to quit. I had like 100 hours on one character in Oblivion and had only completed one guild.
Also, get it through your head that you don't need to pick up everything and sell it. These games have lots of items, every enemy drops each part of their equipment and you need to resist picking everything up and selling it. In the beginning of the game you will be strapped for cash but soon after you will have more cash than you know what to do with so don't loot everything you see.
Finally, I still believe you should do all the side stuff before getting bogged down in the story. If you start one quest tree, complete that tree before going to another, but make sure you don't get stuck in a quest tree, no matter how much you might want to explore, keep doing quests, you can always go and run around later.
So really, big picture, I don't like the games because I play them a specific way, my advice would be to do the opposite of what I do which means keep moving.
Note about mods for people who have the PC version:
The mod argument is tricky. First and foremost, don't get mods that extensively modify gameplay, get the ones the FIX THINGS and the ones that make things look better. The UI mods are important, and being huge games, the unofficial patches people make are life savers.