I've been meaning to do a startup for over a year now, and have spent that time observing the world around me and figuring out what I think are genuine problems that I think I can solve. I finally quit my job a little while ago to pursue these, but am now stuck in a predicament I cannot seem to find my way out of - I seem to have too many possible ideas and no logical way to choose among them! They all seem like that have potential, but they are all quite different from each other so I cannot work on all of them at the same time. I know it's hard to really give specific advice on this, but I'd love to hear from entrepreneurs who might have gone through something like this before. Should I try to do an analysis based on some framework, or just follow my gut on this? Or is there a better way?
This is a broad question, which would really benefit from a much deeper understanding of where you are at and who you are as a professional, but here are a few tips:
A good idea will solve a problem. You want to be building a pain killer, as opposed to a vitamin.
Once you feel like you have a problem to solve, you should validate your idea. Here are some simple tips for validating your idea: http://www.startuprevival.com/7-ways-to-validate-your-idea/
I also recommend entrepreneurs to test the market by setting up a landing page and sending some traffic to it. Unbounce is a great tool for building landing pages.
With a modest budget (just a few hundred $) you can drive traffic to your landing page through Google Adwords. Try and get people to fill out a lead form or sign up for a trial of your product. If you get some leads, it will help you understand if there is demand for your idea. If you don't, it could mean there isn't a strong demand.
You could also buy some market research data using a tool like Survata.
Once you have a validated idea that solves a problem, make sure it is something that you have 1. an interest in and are passionate about, 2. you could execute on with your skill set.
There are a lot of great ideas out there that solve problems. But it's important to make sure it's the right fit for you.
Best of luck!