I have an app for an idea that will require around $100K capital to completely build and launch. Should I try to raise money or figure out a way to invest my own money?
If you just have an idea, chances of being able to raise money for it are slim. You will need a prototype built, at the minimum. Usually startups try to raise seed capital when they have the initial version of the product built, and have some early traction.
Like @Nishank said, you will have a hard time raising money without a prototype.
I also would like to add that 100K$ for just a mobile app is insane. What makes you think you'll have to pay so much? Most experienced developers can get a prototype running in a single weekend by themselves, so you could find someone to do it for much less than 100K$. Server costs etc should also be very low initially, even free.
First of all, $100k is a huge amount for someone to invest in a startup. As we already know that only 1 out of 10 startups taste the sweetness of success. Rest of the startups either sell their business or undergo heavy loss.
In your case, it seems you haven't even built your business model, if yes, then its good but still not enough to invest that much amount individually.
Normally, people who have already built some of the segment of their project which gives them pretty much of the estimation of the project's success rate.
Here, $100k means that your idea has to do something on a big scale, so you also required a big team. I would suggest you prepare your business model and prototype, then represent it to the investors.