What in your life would you pay for, that does not exist?
What do you know others will pay for, that does not exist?
What is your unique intersection of talents, interests and experiences, that might allow you to find a new angle on something?
Don't start with the idea of "a startup". Look for a way you can make life sufficiently better for a sufficient number of people/companies with sufficient ability and willingness to pay. The startup is the vehicle by which you trade your solution for money.
What do you know others will pay for, that does not exist?
This is especially important. Don't just try to solve an arbitrary 'problem', think about people that you're around often, what they do, what they complain about. These will be your first testers / potential customers, and you'll need them to keep you working towards solving something that actually needs to be solved.
I agree that the idea is secondary, as it usually changes. I'd really recommend you read Paul Graham's essay to understand his arguments that ideas are secondary, that co-founders matter a lot, and why you should/ should not start a startup.
After delving into these ideas, choosing the actual idea to pursue, I found that using swot (http://en.wikipedia.org/wiki/SWOT_analysis) analysis can be useful. Several questions from the application for YC are also useful (and can be categorized into Strengths, Weaknesses, Opportunities, and Threats) for fine graining: http://files.dropbox.com/u/2/app.html. Note that this application form is old, but the questions are still relevant.
This is part of what holds me back. I have a lot of ideas for startups but I'm not sure that some/any of them will be revenue-generating.
Maybe a better starting point for me is to post some of the ideas and see what kinds of responses those get.
However, picking a project that will generate money does not necessarily mesh with making the project that is most interesting to me, which adds to my confusion.
It is entirely sensible not to go ahead with a startup if you're not sure about whether and how it would be a successful business. You'll never know for sure, but it makes sense to have a good idea of whether you have a market, for example, before putting in all the work of building the thing.
Putting out your ideas and getting responses is a good way to start. Start an ASK HN post, explain what you're doing, and put each idea as its own reply to your post. Then people can reply to each idea separately, and you'll get a conversation on that.
Remember: the idea itself isn't always fascinating to hear. Basecamp - project management for teams; Posterous - simple blogging. And so on. So don't worry if your ideas get an "It's been done" response. What matters is whether there is room in the market for you, for your price point, for your feature set, for your marketing strategy, and so on.
What do you know others will pay for, that does not exist?
What is your unique intersection of talents, interests and experiences, that might allow you to find a new angle on something?
Don't start with the idea of "a startup". Look for a way you can make life sufficiently better for a sufficient number of people/companies with sufficient ability and willingness to pay. The startup is the vehicle by which you trade your solution for money.