Thank you very much for the help. I purchased the upgrade to 10.11.6 (El Capitan) and will do the upgrade shortly.
If I understand you correctly, I will be able to replace I-Photo with PHOTO in the upgrade to 10.11.6.
Yes, iPhoto will effectively be replaced by Photos. The Photos app will have a rainbow colored "flower" in a white circle icon and should automatically appear on the Dock (I believe). When you open it, it should automatically upgrade/update your old iPhoto library to a Photos library.
If this upgrade is successful, would you recommend upgrading to Sierra 10.12?
There are typically two basic reasons to upgrade to a new OS...1) get new features and/or 2) keep getting security and/or bug updates. For the former, that is something you would need to decide...i.e. whether you consider the new features something that you want to do. For the latter, since Apple tends to keep supports the two previous version of the macOS when they provide a new version, you can stay with either of those two older versions (in this case 10.10 and 10.11) and still get at least security updates. If you are more than two versions behind, then it is usually a very good idea to upgrade to at least one of the versions that still get security updates. Beyond that, it kind of goes back to #1.
The points is that since you will be at least up to 10.11 (which still gets security updates), then it is really something you need to decide based upon whether you want the new features. Here is at least one webpage that describes the major new features:http://lifehacker.com/all-the-new-stuff-in-macos-sierra-1786817117
I can personally say that I typically wait at least a month or two before I upgrade to the latest version. I do this as it allows Apple to work any kinks out of the new version. In other words, I don't want to be Apple's "test dummy". I also do this because some of the utilities and Mail plug-ins that I use may not initially support the new version when it is released. For example, I am just about ready to upgrade to Sierra (aka 10.12). I believe all of my utilities and Mail plug-ins have versions that support Sierra (I did have to pay for some upgrades) and I believe Apple has basically worked the kinks out of the new version. There is at least one of my Mail plug-ins that is no longer supported and will not work with Sierra, so I am debating how important I consider that Mail plug-in. FWIW, most major "productivity" type programs (i.e. MS Office, Photoshop, etc) will typically work with new versions with no problems. It is generally more "low level" type programs (disk utilities, other utilities, Mail plug-ins, etc) that might get "broken" by major new versions of an OS.