Having recently started DMing my first P&P game since a few basic adventures at lunch in high school. I can say with supreme confidence that the most important factor is collecting players that want to play. If anyone is on the fence about enjoying the concept of role playing, it will only create tension and pull everyone out of the game.
You've made a very good choice with the Red Box. It lays out a lot of the game clearly and holds your hand through making your first characters. As Loptr said, feel free to toss out any rules that you don't really get and bring them in one at a time until you and your player/s are comfortable with them.
I would go so far as to even avoid combat your first time out. Focus on story, on helping your player/s become their characters, and also on presenting interesting people for them to interact with. Only bring in the more complicated aspects of the game as the players all feel ready to try them.
Now, as for being fun with just one player. That's totally possible and I've been playing side games with just 2 players. The rules weren't designed for it and it can mean that building battles is harder, and it also means that you, as the DM, need to bring a lot more of the interest to the game. You need to provide all of the people for the player to talk to. You need to provide all of the setting. No one else is there to chat with the player while you think up what the NPC she just talked to is.
One additional piece of advice. Be unexpected. Be different. Don't be boring. Which means don't plop your player's character at the mouth to a cave, and have them sneak past a sleeping dragon, and so on. Think up something fantastical, something that the player hasn't seen before in a million other forms of media. For my game, the setting is Earth 100,000 years hence, after being split in half by a God which reawakened magic in the land.