Of course, I've only played through the game like twice...
But in both Morrowind and Oblivion, I've chosen Bosmer each time I played... I dunno why, I just like that race the most. And going marksmanship is easy since I can often kill enemies in one or two hits before they even get close.

I am bored and considering playing Oblivion again. I want to mix it up this time though.
I've used the companion Vilja in all of my playthroughs (got into Oblivion kinda late) and she will again be present at my side (a strong melee character... or ranged if you set her up that way... with good Restoration skills).
I want to make a melee/magic character and actually get up close and personal.

From what I've seen, it doesn't really look like it's that difficult to be good at melee. I've played around with melee on my Bosmer marksmen before.
The harder part is Magicka. I always had super low magicka on my Bosmer archers and that seriously restricted the type of spells I could cast.
So, I was thinking that for my new character, I'd make a Breton? Female Bretons have +10 Intelligence and Willpower but -10 to Strength/Agility/Endurance. Could counter that with The Warrior birthsign and just have +10 Int/Will and -10 Agility...? Or maybe go with a different birthsign?

Also, which skills do you suggest for my main skills?

It's nice to think outside our boxes. I've only played humans and elves, for instance, but lately I've been toying with the idea of making a savage lizard man, who never goes into cities and murders any NPC in his path. No quests, either. I don't agree with Argonians speaking the same language/having similar lifestyles to humans & elves.

Bretons are fun to play because of the eventual bottomless pit of magika they possess. I'm doing my third one so far. Can't really recommend majors because I like playing major skills that don't get used much. Birthsign depends on what you're trying to accomplish, and I don't know enough about all that "efficient leveling" stuff personally.