If you only have one new player, I wouldn't worry too much about the game being "too hard" for them. I think we often make the mistake of thinking people who haven't found board gaming are stupid or something. Really, there aren't all that many skills you lack before you bust out your first real game. It doesn't matter how many games of BSG you've played - you're not going to be any further ahead of Joe the Plumber when the gang busts out Twilight Imperium for the first time. I honestly think it's kind of insulting to assume it's a bad idea to play "complex" games with new board gamers. I started a guy on BSG and Twilight Imperium on the same night, and he did fine. The tricky part is really in convincing people they want to play in the first place.
That said, I don't recommend BSG with 4. 5 is ideal. Go for 5. But if you really want to play it, feel free to play 4. It just won't be as good.
If you are looking for something "Rules Lite", Ticket to Ride is a good choice. It's also a good gateway game. Better than Catan, which it now outsells. There's enough random chance to keep it interesting, but enough player agency to make it fun.
In a similar vein to Ticket to Ride is Through the Desert. It comes with camels. Camels! I notice that this "Boardgame Cafe" doesn't have it, even though they have several versions of CSI: the Boardgame. Heathens.
Chaos in the Old World is the best game to bust out when you have exactly 4 players. You'd be remiss not to play it. You can't play it with five (unless you have the expansion), and it's not balanced for three. Play it quick. Knowledge of the setting (which I don't have) is not necessary.
If you want to go for heavy co-op, Lord of the Rings is good. You can play as Hobbits. Fury of the Dracula is a good semi co-op, too: Everybody teams up against Dracula.
I have a certain bias, in that I love BSG and hate Shadows Over Camelot, but if you're passing on BSG, I would not suggest SOC. They are about the same on the complexity scale (SOC has more boards you need to set up and actively place tokens on and keep track of; BSG involves the use of multiple card decks). There is a minority of people (including one or two notable bloggers) who will militantly defend SOC's honour as a game that is still relevant and/or good. This is true of everything. Unless you've got a lot of experimentation time, it's best to stick to what you're statistically more likely to enjoy.
I don't recommend starting out with "casual" games like Apples to Apples, Cards Against Humanity, or even Munchkin. It's really easy for new board gamers to get stuck in a rut with those ones, since they take about thirty seconds to explain, lack regulated end times, and don't let newbies in on what they've been missng all this time. A game with some depth to it (such as Ticket to Ride) is a far better entry.
A previous poster mentioned that Game of Thrones is a bad choice for new players. If you've played one or two games of Risk, you are ready for Game of Thrones. If your players start hankering to get into Diplomacy for some reason (probably reputation), suggest Game of Thrones instead. GoT has borrowed heavily from Diplomacy, but has made it far shorter and filled in some of the gaps. This is the most controversial thing I say amongst the board gaming club I run at my university: Unless you're playing online, you're better off playing Game of Thrones than Diplomacy. Game of Thrones is Diplomacy. But it's better. If you hate Game of Thrones, you're not going to have any luck with Diplomacy.
Though I notice that GoT is not on the list, so it's a moot point.
I wouldn't recommend starting with it, but Panic Station can be fun. It's like John Carpenter's "The Thing" in theme and mechanics. The downside is that it has some glaring holes in its design. It can still be fun despite this problem, but if you have people at the table who are grumps, I'd give it a pass.
Merchants and Marauders is wonky but ideally suited to four players who like pillaging.
When your brain goes to mush, you really can't go wrong with Cash & Guns. You actually literally can't. I've played a lot of board games with a lot of real douchebags at the university, and they've never caused a problem over this one. If the other three people suck for some reason, just bust this baby out and you're good to go.
If you pop down to 2 players again, here's a whole bunch from the list that I would suggest. Most 2-player games tend to be more complex than games with more players, but still do-able (and often easier, since you're less likely to get a rules lawyer the less players you have).
Twilight Struggle
War of the Ring
Hive < --- Hive is short, easy to play, and full of depth. You'd be foolish not to try it.
Memoir 44
Mr. Jack < --- My girlfriend and I play Pocket and Normal-Sized (which have different mechanics) and love it
If you really get into it, you might have to look into buying your own games, though. This Monopolatte place doesn't seem like it has the best selection (BSG is missing both the Pegasus and Exodus expansions, but they have the "unofficial" Daybreak Expansion? What?). Sometimes you can play at the FLGS, or at least post bulletins looking for other players.