Early on, his health costs are high enough relative to his total health pool that his clear hurts pretty bad early on. You may find it worthwhile to invest a couple points into utility to get alchemist for better potions (only takes 5 points) and then go either 4-21-5 or 0-25-5. If you take points in offense, grab 3 point in attack speed and then the butcher mastery (speeds up clear a bit). If you go 25 defense, pick up every single health regen mastery, every armor buff, and every health buff, then just get whatever else suits you. I'm not that great when it comes to runes because I don't own too many of those and don't have specialized pages for all my champs, but I would definitely suggest flat armor seals and if you have a hard time with early clears, flat armor Quints as well.
Item-wise, always rush Juggernaut, and then (assuming you aren't going for a weird magic pen build) choose either an armor item or an MR item. I prefer going armor first when possible since it allows you to clear super healthy. Good early armor items would include
(tons of health, good armor, and a great passive that helps with ganking for Mundo)
(if they have a strong right clicker like Yasuo or Jinx) and
(after the changes, it actually deals the most damage in very early game as a stand alone item, ironically enough). Good MR choices would include
(excellent synergy with your passive and ult, great sustain overall)
(great against an AP heavy team if the support isn't getting one)
(mostly for tenacity, good if they have CC and a fair amount of AP).
is a good item, but after the upcoming changes, it is mostly good against crit heavy carries and is better as a mid-late game pick up if you do grab it.
is less than optimal unless you need to avoid a really significant spell like Annie's Tibbers, otherwise the other MR items are just better on him.
is a great item, but after the changes coming next patch, you should only look into getting it once you have 3k HP since the main passive (15% max health as HP5 when out of combat) only turns on when you have more than 3000 HP. Titanic Hydra is another great option that will be coming next patch, it gives you good wave clear, amazing damage for a full tank, and a nice bit of health regen as well. Sterak's Gage is another good one, but it'll probably be a bit more situational since you won't make great use of the AD portion, but it does fit Mundo's play style of running in full throttle and soaking damage to hell and back before popping ult and doing it all again. It's like having a third life.
As for actual clearing, I'm not gonna be able to be much help. From what I've seen, starting with cleavers and killing Gromp is the best start, and then you take burning agony and clear wolves before going and taking blue, backing, and then clearing the other side. I've also seen people just start Red with burning agony and then smite to get a lot of HP back, which can work too.