Ok I used "Twenty Ten 1.2 by the WordPress team" and made 2 changes. I changed the 940 x 198 image and on many pages chose the page attribute template with "one column and no sidebar". Other than that, I have been busy with content.
I now see that I can decide the size of the images. In this, I could set the size to 940 x 198 and choose a theme without a picture at the top. This way I can place a different picture at, or near, the top.
I hope that a few ways to do this might be presented here. I do have an extensive background in programming but only scarcely looked at PHP.
I am not sure what the consequences will be but I may have just answered my own question (-: I will look for a theme without a picture at the top and see if I can place my own image.
Meanwhile I will continue to look for suggestions here.
Thanks for the response.
P.S. Adding a note after I just posted that note: I see only one other template available. Am I missing something?