Everyone will have his/her own opinion on the matter. One way might work well for one person and another way will work better for another. The important thing is to stay safe and know your limits. I've been snowboarding for six years and this is what I found to work well for me:
It was my third season and one of the lift operators suggested that I try out the halfpipe. The snow was very soft that day, so the conditions were ideal for learning. She was right; the snow cushioned my (numerous) falls, but I eventually started pulling off some jumps. Traversing can definitely be helpful, but so can linking the turns and carving. I learned by carving on a 45 degree angle (not 90 degrees), making a jump as I turned my body, and landing.
Some people have claimed that starting out in the park first is better. In all honesty, I started in the halfpipe first and I was fine. I think it depends on what kind of riding you'd like to do because the type of board you use for the halfpipe should be different from the board you use for the terrain park. This is because you need excellent stability and edgehold when tackling the halfpipe, which requires a stiffer board. The terrain park, on the other hand, has rails, boxes, and many other obstacles that require a board that can take punishment. A flexible board is good for absorbing impact. Also, you don't want to have sharp edges in the terrain park because sharp edges will catch on rails and such (however,you want to have sharp edges for the halfpipe).
It is important to land properly, but you don't have to practice in the terrain park to do it. You can easily find a wall on a regular slope to practice going up on and can even try springing up over small lumps of snow. Again, when the snow is soft, you can practice jumping on the halfpipe. If you're concerned about falling, you can purchase some body armour, but I can honestly say that I've never worn any and I was fine practising (I have never seriously injured myself when snowboarding). It's your call.
A couple of tips: be sure to bend your knees to absorb impact, watch some videos online and read some literature on the subject, and (if you want) get an advanced lesson. First and foremost, stay safe.