I'd suggesting moving
everything to Vanguard. Any old workplace plans and old IRAs (especially the small ones at the credit unions). Call Vanguard and have them help you do this - there's too much room for a convenient "misunderstanding" (especially by American Funds) that will lead to a tax nightmare and loss of tax-advantaged space. Vanguard will transfer the assets
in kind, and they'll initiate the transfer - that is, a pull not a push. Just have the statements from those places in front of you and they (Vanguard) will walk you through it.
Remember, you're doing a rollover, not a withdrawal. - that phrasing is important.
For others following along: Banking institutions are generally a poor place to invest; insurance companies are even worse. These places are great for banking and insurance, respectively, but are terrible for investing. High-cost brokerages (American Funds, Edward Jones, etc) are also worth avoiding.
If you don't know what to invest in, pick an appropriate target date fund. You can always re-allocate it from there - or, once it's all in one place, make a post here, letting us know your desired asset allocation (% bonds, % stocks in domestic, etc) and we'll help you set it up.
One thing that confuses me is that TIAA-CREF pushes annuities, which I don't entirely understand. My instinct is that this isn't the best way to go, but how do I learn what I need to know?
Never invest in something you don't understand. Annuities are nice for guaranteed income if you can't manage this yourself, but they're a lot lower return than even a simple auto-pilot target date fund. In short, I don't think they're appropriate for you in this circumstance - you're clearly capable of understanding this stuff and doing it yourself.
Check out the
Bogleheads' Investing Startup Kit as a great way to learn about it. I can suggest some traditional paper books, too, if you prefer.
If I do the rollover, is it better to wait (till the end of the year, e.g.), do it ASAP?
Do it ASAP. Rollovers (traditional to traditional, Roth to Roth) are not a taxable event and have no annual limit. Just pick a weekday or Saturday morning when you have some time, call Vanguard, and they'll walk you through it.