Most people will tell you "ideas are a dime a dozen", or "share it with the world and get feedback", or "it's not about the idea, it's all about the execution". I totally disagree with these perspectives; these are just dogmas, things that people believe and repeat because that's what everybody else is saying and who wants to take the risk of going against mainstream? Every dogma has some truth to it, as well as limits.
Now let me clarify my point of view: I think that many business ideas are actually worthless, that some ideas are good and that really really great game-changing ideas are very rare. So if you think you have a really great idea, that's awesome. Now move on to the execution phase.
First: investors that can actually help you won't sign any NDA: it just doesn't make sense for them because they expose themselves to future lawsuits.
Second: if you have a great idea but you don't have the resources to put it together, I'd recommend against meeting with investors when you're just at the idea stage. Startup investors know other entrepreneurs and if they really like your idea, they'll probably share it with people they know to discuss its validity, and that's when you'll be at risk of seeing someone else execute on your idea. Investing in a startup is about trusting the founders and if an investor doesn't know you but knows other entrepreneurs, then he's more likely to fund people he knows than to fund you when you're just at the idea stage because he'll most likely think "ideas are a dime dozen and it's all about the execution anyway".
Third: let me tell you a story. At the end of 2011, I applied to a startup incubator that was vetted by Silicon Valley entrepreneur/investors/mentors. At that point, I wasn't at the idea stage anymore but still had some way to go to get to a finished working product (I'm actually still working on it.) I had the concept, the UI and the coding was about half-way done. Part of the application included an NDA, so I thought there'd be some kind of protection and I applied, but wasn't selected. Then, a few months ago, I just discovered a startup that released a product with the exact same idea: out of nowhere (actually, out of a totally unrelated product and unrelated personal experience), the founders had somehow pivoted into the space I'm in, with the same innovation, and yet their background just didn't seem to fit the story. In fact, their website read so similar to my application that I felt sick to my stomach reading it. But of course, a) I know I'll probably never be able to prove that the founders were connected to the incubator or that they saw or heard about my application and b) I might actually be wrong about this, even thought my intuition tells me otherwise. Like you, I think my idea is truly game-changing and addresses a very large target market, and so did some VCs who ended up investing over 20 million into it (at least I know I'm onto something!). But at the time of that application, I had just the idea and a half-way finished product. Now I'm not suggesting that all investors and incubators look for innovative ideas to execute on, but I'm sure that it happened, even though of course no one will ever say they've ever taken part in such practice. So don't be naive and when doing business, be aware of other people's interests, not just yours.
So, based on my personal experience, here's my recommendation to you. You say that the idea is simple so may be you can put it together yourself, or may be you need a co-founder to help you code it. In any case, I recommend that you build the product first, before talking to investors. To address your concern about how secure sharing a business idea is, just assume that you're sharing it with the entire world. Then, when you've got the product finished or nearly finished, go talk to investors to get the funds you need to launch and scale. And keep in mind that there's some truth to every dogma and I really do think that execution is the second side of the coin: you need both a great idea AND great execution to succeed. If you only have one side, then you're missing out: great execution on a bad idea or great idea but no execution both lead to nothing. So in terms of executing your idea, I recommend putting the product together, testing it with a few people who aren't into the startup world but who are part of your target market, and then talk to investors when you reach that stage. Of course, all this assumes that you actually have a great idea.
Ideas and imagination are the most valuable ingredients of entrepreneurship and while your ideas might be copied, no one can take away your imagination.
For sure, some people will disagree with me about this answer, but I don't care about being politically correct.
Good luck on putting your business together: now that you've got the idea, focus on the execution.