I have a few ideas on what elements a good 'starter' RPG needs, and I've been reading through a number of games in order to find more ideas to add to that list. But I'll start with some of my actual play experience with starting new players on RPGs.
To start with the start, my own (and I suspect many others') first RPG was the venerable Dungeons and Dragons. I myself started out with Advanced Dungeons and Dragons Second Edition. I had many a great game of AD&D and it will always hold a special place in my heart, but I have begun to expect that it hooked me into RPGs more because of who I am than because of the rules themselves.
When I first read through the Players Handbook, I was just a kid (nine years old). I found the rules bewilderingly complex. Once I actually sat down and played, that helped a lot, and when I reread the rules two or three years later, they seemed amazingly simple. For one thing, I'm sure my own increased maturity and mental faculties helped, and for another I'm sure that having play experience to map the abstract rules onto helped a lot, but recently I've started wondering if my initial reaction was solely due to my youth, or if perhaps older people with no prior knowledge might find them similarly bewildering.
The Dungeons and Dragons rules, of all editions, show their tactical wargaming roots, with a strong focus on multiple exciting things to do in combat and detailed rules to cover them. Fourth edition has gone a long way towards making these rules easy to grasp, provide balanced play, and to be pretty darn neat, honestly. But as much as I love detailed games and rules systems, I don't think it's any of these features that made me grow to love the hobby. THAC0 never fired my imagination, hit dice didn't keep me coming to the table, and encumbrance rules certainly didn't make me think I wanted to branch out and try other roleplaying games.
It was always the roleplaying itself that gave the rules their spice, the imaginary people and creatures in their imaginary worlds that kept me coming to the table and rolling those neat polyhedral dice. The rules were a means to an end, albeit an interesting means. They were a tool for fleshing out personas and interacting with their surroundings.
It wasn't very long before I was introduced to one of my favorite RPGs of all time, which produced some of my fondest in-game memories and stories, and yet was one of the least serious approaches to roleplaying I've ever seen. I'm talking about Teenagers From Outer Space (R. Talsorian Games, 3rd Edition, when they got all the zany Anime stuff).
Teenagers From Outer Space (TFOS) is a light hearted comedy roleplaying game about, well, teenagers, many of whom are from outer space. It helped that I was introduced to it by a talented and entertaining game master who made improvisation seem effortless and who seems to have been made to run wacky, alien-filled John Hughes style stories. He also frequently used TFOS as a 'gateway drug' into the wonderful world of roleplaying games.