I would recommend either TwentyTen or TwentyEleven as great, basic starter Themes. Both include a few nice bells and whistles, but for the most part are straight-forward, simple Themes.
However, can you clarify a little more specifically what you're looking for? For example, you mention that you are looking for a Theme that includes "only the files needed", but then list two entirely unnecessary files,
single.php and (especially)
Do you want a Theme that is easy to modify? Easy to override with a Child Theme? Easy to grok the underlying code? What are your specific needs?
That's what I mean about being more specific:
- How are we supposed to know what is "useless" for you?
- What Theme template files do you consider to be "necessary"? Especially considering that only 3 files are truly "necessary" -
comments.php - if you consider other template files to be "necessary", then you'll have to communicate your needs more clearly.
- What "main functions" do you want the Theme to include?