You can change masteries anytime other than while playing a match at least. You can change them out of matches by going to your profile, and you can change them in the champion select screen immediately before a match begins. Just keep an eye on the countdown ticker, as you wont benefit from any points still unallocated when the match begins.
Bot game IP rates have been altered. The IP you gain now depends on your summoner level, so newer players receive full points, and older players receive less and less. The old bot games per day limit has also been removed and replaced with a timer limit. You get something like 2 hours a day of bot-games before they cut off any IP or EXP growth. They really want you playing against actual people.
As for favorite champions, I tend to go with fast, squishy, and high-damage characters. These tend to be ninjas ans assassins, but not casters (as they tend to be slow!). So that means characters like Yi, Akali, Ashe, Warwick, and Nocturne. Sometimes I'll also migrate over to heavier champions, as long as they are still fairly fast or have mobility options, such as Jax or Lee. I rarely ever play dedicated tanks, support, or casters, as I don't have the mindset for it.
I'd say go with Cho, if you like him. Sure he has a skillshot, but it's an AOE, and failing it isn't so damning as some other character's skillshots. You also won't improve without practice!
Avoid invisibility for now. Not because, as KraziKarl pointed out, Eve and Twitch are bad characters, but because all three require some exceptional skills to use properly. Any champ can be effective if you develop a knack, but it's a lot harder for those three.
In regards to my favorite champs, the easiest to play would have to be:
Ashe - Despite her Skillshot Ult, which takes some real practice, her other abilities are all noob friendly
Warwick - You can jungle with him at summoner level one, just not very well. Otherwise, his abilities are pretty noob friendly as well.
Jax - I'm on the fence. He's a very aggressive champ, which often leads to new players getting themselves killed, repeatedly, but he's going to be the safest one to give hybrid builds a try in, and his passive has some synergy with the noob's general tendency to only stack damage items.
As for the others, Yi is just too weak these days and too easy to shutdown. Akali is a great champ, but takes practice and downright deserves a full rune set. Nocturne... well, there are just a ton of new Nocturne players who are downright terrible. The game doesn't need another! Ditto goes for Lee, who also has the dedicated distinction of having a schizophrenics array of skills requiring a degree of timing.