In order to validate a start-up idea, is it better to have a landing page, drive traffic, collect emails then engage with customers, or simply do customer discovery, reach out to idea customers, and interview?
There is certainly value in starting customer discovery interviews. And no reason to wait for the delay that creating a landing page and waiting to collect emails would take.
I would just advise that you get clear on your hypotheses about who your target customer is so you talk to the right kind of people. Personas can be a good tool for capturing your assumptions about target customer.
A key concept is the different between problem space (understanding customer needs and pain points with how they're getting their needs met now) and solution space (evaluating your idea for how to better solve those problems).
You can go pretty far with customer discovery to understand the problem space. At some point, though, you will want to transition to soliciting feedback on some solution space artifact that represents your solution.
A landing page is good for testing your value proposition and messaging. At some point, though, you'll want to transition to testing a prototype of your product (e.g., tappable or clickable mockups using InVision). I'm a big believer in testing with prototypes before you actually build your product.
I've actually created a 6-step process for defining and testing a new product idea, which I describe in my book The Lean Product Playbook: http://amzn.to/1EYCUdP
I've also given several talks that you can check out at http://dan-olsen.com/speaking/
It all depends on what your idea is and what stage you are at in idea formation and company formation.
Set-up a call, share more info, and I'll give you my advice.