I need help on choosing the correct Adobe software. I need the ability to manipulate, delete and edit images, diagrams or text and add geometrical shapes and designs to the image. What Adobe software works best for what I have described?
Photoshop or Illustrator will do those but each have areas where they work better. Are your images raster graphics or vectors? Photoshop is more geared toward raster graphics but can work to some extent with vectors. Illustrator is more for vectors but can work with raster graphics to some extent. If you get a subscription to the Creative Cloud, you get both programs plus a lot more (Adobe Creative Cloud desktop apps | Adobe Creative Cloud , Adobe mobile, iPhone, iPad, Android apps | Adobe Creative Cloud). I hope that helps.
In addition, you can get a 7 day trial of each. Try one for seven days, and then the other to see which better suits your needs.
Also, watch these free tutorials to get an idea of what each does. They include Try-its.
What file types are you working with?
How will these images be used -- on the web, high quality print or video?
If your native files are JPG, Bitmap, PNG, TIFF, or PSD use Photoshop. The learning curve is steep but PS is the industry recognized standard for image editing software.
As Myra said, Illustrator is the better choice for creating vector graphics for print and SVG output -- i.e. logos, text, flow charts, diagrams, graphs, icons, advertising, etc....