Thank you for your quick answer. I did not know that I had Yoast Twitter Card support turned on, so I’ve turned that off. As for the size, I think the images really need to be 2:1 in order not to get cropped. 280×150 or any multiple of that leads to a little bit of cropping. I can’t confirm that 100% until I make a new post, but I do know that 280×150 will be cropped.
The major piece that I was missing was what to do with the custom field information on each post. I had it set up correctly in the Twitter Card option, but I could not figure out what the next step was – how to indicate which picture to use in each post. I finally put it all together.
For anyone else who can’t figure it out: Upload the image that you want to use to your post. You don’t have to place it in your post, you just have to upload it and get its URL.
If the Custom Fields editor is not showing for you in the WordPress editor (it wasn’t for me), you’ll have to go to “Screen Options” in the top right corner and add it. Click “Enter New” under “Name.” Then, put “images” (or whatever word you set up in the Twitter Card options) in the “Name” field, and put the URL of the image in the “Value” field. Add the custom field, then update or save your post, and the correct image should show on Twitter.