People often think the less active abilities a hero has, the easier it is. I don't think that's the case. The game is hard, and that won't change anytime soon. So instead of just finding you simple heroes, look for heroes that you can benefit from as a whole.
Lets go by role, and you can choose from there.
Carry: Viper, Dragon Knight and Riki. Viiper is pretty straight forward. Read the skills. Dragon Knight isn't too complicated, and it gives you a chance to learn a hero that has range and melee all at once. Riki, just because his ult gives you freedom of movement, which can give you time to see whats going on around you, and (hopefully) figure out better positioning.
Support: Dazzle, Lich, and Lion (sorta). The problem with support heroes in bot matches, is you are pretty much relying on an AI to do the important stuff. So you probably won't see much success with these against bots. But anyways, Dazzle is about timing. Nearly every spell in the game has an attack animation that must happen before the spell takes affect. His Shallow Grave is a good example of this, and will help you understand when to use it, and when it is too late. Lich is all about the denying and ult, as far as learning goes. Try to only use the ult when enemies clump together, and the less creeps nearby. His E denies an ally creep for mana. Denying a creep to an enemy denies them some EXP and gold. Which is really good at the start of a game. Lion is more of a ganky kind of support. He has crowd control and burst. I picked him mostly because you can support and still blow stuff up. Not much other reason.
Other heroes you might enjoy:
Antimage - His blink, mainly. Makes it easy to survive stuff. A few of my newb friends enjoyed him because of that.
Axe - Tanky, but fun. He was one of the heroes I started on. He is pretty easy.
Zeus - Blows things up. Everyone enjoys him, for the most part. If you want to nuke stuff, try him out. He is squishy, though.
Shadow Shaman - He does pretty much everything. Lots of CC, a good nuke, and a great ult. I also used this guy to practice.
Venomancer - Pretty easy hero. You can build him support or damage. Get one level in his Q and W, and then max his E. Then spam his E, and enjoy.
Skeleton King - This guy is super simple, but he is a carry and needs to farm well to be effective. Ult gives you two lives, so new players enjoy him.
As always, opinions differ from dude to dude. Some may or may not agree with this. What I can tell you, and what everyone else will agree on is: Don't let a few losses hurt your feeling over the game. This is a game that relies on all five players to do well. When one fails, usually the rest will follow. This is not an easy game, and we all sucked when we started. When you start playing with players, let them know you are new, ask them if they can give you pointers or advice. This will usually calm the ragers down a bit (but not all the time). You may not want to use the voice chat, but I would suggest getting used to it earlier rather than later. Also, take some time to understand the lingo. That will make things far less troublesome for you later down the road.
Bounty Hunter is purrddy good. He needs farm, so make sure you farm. He can go on any lane. You can roam on him too, if you are confident your team can help setup with ganks.