Generic templates are generally easier if you're building a site around them, rather than try to make them work with someone else's program.
If you're not capable of making a template, then it probably wouldn't be much easier to modify one to work with something else. Luckily, there are so many templates out there for the common applications, it's usually not a big deal.
Also, it's usually easier to tweak an existing template/theme/whatever than to create or modify one to work. Using Wordpress as an example, there are a lot of sites out there that have done nothing more than replace the main header image with their own (default theme), which adds a unique look to an otherwise standard layout.
You can usually just find the area you want to change in the source code, then find it in the template files or .css files and make your changes.
Of course, like anything else, "easy to change" often means the same as "easy to screw up." So it's best to make small changes, check the results and repeat, until you're used to it.
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