I haven't played LoL and Dota 2 was my first game in the genre, but here are the heros I found easiest to play. Most of them are quite tanky (or can escape) to cover for mistakes that might occur while learning:
Skeleton King: With 3 passive abilities, all you need to learn with him is when to stun and when to charge in and tank and when to withdraw (don't go in 1v4 :P). He's very tanky and can jungle quite well as well.
Dragon Knight: Also quite tanky, has one of the longest stuns in the game. Dragon mode makes your stun ranged, which makes it even better.
Juggernaut: Blade fury makes you immune to magic and is great for both starting a battle and running away. Healing ward improves survivability and omnislash will solo gank most heroes.
Ursa: Very easy to learn. Once you get the hang of jungling with him, you'll easily be the most powerful member on your team and win most pub games. Make sure you get a blink dagger sooner rather than later though.
Queen of Pain: Lots of spammy skills, not heavily reliant on items to be good since primary source of damage is from abilities. Blink is also great to have.
I also highly recommend trying out a few coop vs AI and/or just play on a match with you + 4 bots against 5 bots just to learn the items and skills.
Images courtesy of the dota 2 wiki