So far it seems that my main problem with playing Mundo is getting ganked early on and therefore lagging behind in XP/GP and thus feeding. Any tips?
Mundo is squishy early on. You just have to be careful until you've built up a bit. Cleavers are everything to Mundo early game. They're his defense and his offense. Even level 1 ultimate doesn't do much for him, besides more sustainability in his lane. It won't cause rapid enough regeneration to save you from a gank like it will late game, so its only defensive use is the speed boost.
He's very much a mid-late game champion (assuming you are building mainly tank items on him). After you have boots/spirit visage/warmog's, you really start to shine. Until then just whittle away at the enemy from bushes or a safe distance with cleavers. If you're pushed out to the river in your lane and there are enemies missing, throw cleavers into the river bush often (from max range) to detect anyone there.
Also, you fear certain champions more than others early game vs late game. Early game, you can out damage most carries with cleaver and masochism, at least enough to kill them 1v1 after whittling them down with a couple cleaver shots. Take advantage of this while you can, because they'll be your biggest threat late game (as usual with carries). What you need to be afraid of early is cc + burst damage. AP Nukes and assassins will tear you apart quickly if they can get you in range, though late game you will be able to almost completely ignore them. Keep cleaver distance between yourself and any such enemy characters, and beware flashes and other such moves to catch you suddenly. Keep your HP high.
You might also think about which teammates you take with you into lane. I find Mundo works really really well with an assassin or other catch/burst damage type character, because his cleavers should be keeping the enemy at half health or less at all times and constantly ripe for someone else's finishing move.
This is assuming, of course, that you're playing Mundo the same way I do. That is, build tank items until immortal, and then build some damage.