Either you start with The Hobbit, or you start with LOTR, so 2 choices.
The Hobbit --> LOTR is the chronological order, although it might present a few continuity issues (not a lot though), and a few other... differences.
LOTR --> The Hobbit is the order most people viewed them in. It works good because Fellowship of the Ring as a movie is the best introduction to Middle Earth there is. However, watching The Hobbit after LOTR is kind of boring because you already know what's going to happen, for the most part.
That being said, seeing as most people have seen LOTR --> The Hobbit, I've never quite got feedback from someone who watches Hobbit first for the first time. That would be interesting, mainly to see if it works.
Also, if you watch The Hobbit first, keep in mind that there is a huge difference in tone between The Hobbit and LOTR. It just doesn't feel the same. LOTR is much darker. And much better. And you should watch them all in Extended Edition.
edit: The movies in chronological order are as follow: 1. The Hobbit: An Unexpected Journey 2. The Hobbit: The Desolation of Smaug 3. The Hobbit: Battle of the Five Armies. 4: The Lord of the Rings: Fellowship of the Ring. 5: The Lord of the Rings: The Two Towers 6: The Lord of the Rings: the Return of the King
edit: Also, the movies have a tendency to get longer as it progresses. If you watch them in chronological order, Extended Edition, the runtimes are: 3h02 min, 3h06 min, 2h24 min (EE not out yet), 3h48 min (3h20 without credits), 3h57 min (3h35 without credits), and 4h23 min (4h01 min without credits)
Every minute is worth it on LOTR though.
First the Hobbit movies, then the Lord of The Rings movies. The Hobbit movies are first chronologically and, even though the Lord of the Rings films released almost 20 years ago, the visual effects really hold up, so it won't be jarring going from newer to older movies. Also, the Lord of the Rings are better films, so the movies will be getting better as you watch.
A lot of people in the thread are saying that you should skip the Hobbit completely, but I don't agree. Sure they're not as good as they could (maybe should) have been, but they are not completely unwatchable. They have some slightly redeeming qualities. And if you watch them first, you will appreciate the Lord of the Rings movies even more!
The Hobbit films are clearly made with the intent that you've already seen LOTR in its entirety. Especially the extended Unexpected Journey, with Bilbo's look-around of Rivendell.
Another oddity of watching them in chronological order is that Gollum goes from being kept almost completely in the shadows, building this air of mystery about him, through FOTR to finally be revealed in TTT. Yet, in AUJ, he's right there, front-and-center, no mystery whatsoever.
And, as much as I didn't see the point of the framing device in the first place, Hobbit's future scenes won't mean anything to an audience that hasn't at least seen FOTR yet.
Similar thing to Star Wars and the prequels, where it could go either way.
In terms of viewing order, there is a very big distinction: the Star Wars prequel ruin the twist of Episode V at least 3.5 films too soon. The Hobbit doesn't do that. Rather, there are many instances where it heightens and deepens aspects of The Lord of the Rings:
Gandalf's demise means more after we've been with him for three and a half movies rather than just one half.
Saruman's betrayal means more after he's fought alongside the Council.
Gimli and Legolas have more depth due to the exploration of their backstories (Gimli's through his cousins)
Finding Balin's tomb has a whole new resonance.
Bilbo's relationship to Gandalf carries more weight.
The extended coda at the end of The Return of the King feels more earned at the end of a 20-hour cycle rather than an 12-hour cycle.
The Hobbit was concieved of to be viewed before The Lord of the Rings. There's a funny moment in the audio commentary where, over a shot of the shards of Narsil, Jackson says it "will come to have a great significance in the later trilogy." All the callbacks to The Lord of the Rings can also work for a new audience in the opposite direction.
Sure, since the filmmakers had already been in Middle Earth for a long while by the time they made their prequels, they don't always bother explaining things as well as they should in An Unexpected Journey, but honestly that elipsis is a good thing! It makes the world more real when Bilbo is talking about the Sackville Baggins and we don't know what the hell he's talking about.