I don't care for 'all rounders' any more, but I used to play them. My choice for such a character would be a Redguard Atronach. Great special power. Great magicka. Great magical defense. Great melee attributes. Strong right out of the box and just gets better. Ultimately, a Breton with the mage birthsign has even more potential in my opinion, but takes more tending at early levels to work on those wimpy melee attributes. Many would recommend a Dunmer since they are well balanced, but I prefer either of the other choices I mentioned. Go with blades and don't shy away from magic and stealth. If you're concerned about getting weak, you may want to focus on the warrior stuff a little more early on, introducing more magic and stealth as your character grows. Trying to get good at so many skills may also benefit from optimizing paid training each level. Marksman and armorer are good candidates to buy training for.
Pay attention to your attribute gains. An atronach can safely ignore willpower. Unless it is a big deal for roleplaying, you can ignore personaltiy. All my characters ignore luck, but there are many players who would disagree. That still leaves and all rounder with five attributes that are important however.
When selecting major skills, you might consider the following: The more majors from the same attribute you have, the harder it can make attribute gains - this only applies to attributes that you are going to increase. Major skills control how fast you level up - some skills level fast (alchemy, sneak for example); others level slowly (marksman, restoration, destruction, mercantile). Major skills can control how high you level simply by not using them; if you intend to 'cap' your character, simply pick a couple majors you don't need to use (speechcraft, h2h I'm lookin' at you).