Hello Mary Lou,
Before I start, I assume that I should start up the newer iMac from its original start up disk. Is there an article which reviews this procedure?
This requires the 10.5 Leopard Installl disks. You will have two original grey disks. or one black retail DVD. Insert whichever media you have.
Start from the 10.5 Leopard Installl disk 1 as per this article,
http://support.apple.com/kb/HT1544
and choose Erase and Install.
After it has installed, further along you will be asked whether you want to migrate your data. If you do, you will need to connect the two computers. Connecting by Firewire cable is a good method, and select which things you want moved. It pays to click on the triangles in that dialogue box and peruse what is available. Just your old User account may be enough, plus your email setup.
what happens when an application I send over needs to be updated to accommodate the newer OS?
I prefer to reinstall third party applications manually by either copying the application's .dmg over later via a USB stick, or once on the internet download the latest version from the developer if one is available. Why? no reason really, I just prefer to first get the Mac OS itself in a good state, and then later add other people's software to it. You may find some software from Adobe can only reinstall from the CD.
Should I do any cleanup on the older iMac before sending data to the newer iMac?
There is no need for that, just bear in mind here is an opportunity to leave a lot of your old stuff behind which is no longer relevant or just like the proverbial pile of newspapers in the corner, leave that behind. Whether moving house or updating an OS, both present the opportunity to question what to keep and what to leave.
I would like to review ... erasing all data from newer iMac.
The erase and install will be sufficient for you. There are no security issues involved here, just a clean sweep that will remove all of your late brother's previous settings, allowing you to customise the account accordingly.
I hope things proceed well for you.