Adobe Illustrator

I want to create graphics, etc. in Adobe Illustrator, then copy and paste them into Adobe InDesign or MS Publisher. I do not want to put the first image. However, when I try to just cut and paste into InDesign or Publisher, the image does not turn (and I just get numbers and text). Suggestions? Should I use Corel Draw instead?

You can not copy / paste from Illustrator and MS Publisher (a program of crap btw.). This is because the content from Illustrator is not a type that Publisher can handle. For this you must export your Illustrator file as an image. Depending on the content which should probably be in PNG format ("representative") or JPG (photo) - based on content. Make sure to export it in the format you need.

Illustrator and InDesign, the other speaks much better with each other as they are both made by Adobe. You CAN copy / paste from Illustrator and InDesign vector elements, but not all types of content can be copied in this way (like InDesign does not have all the features of Illustrator and vice versa). You should try it for simple shapes that you need to be editable in InDesign.

To get the files from Illustrator into InDesign, just to save you. Do file.
Then, in your InDesign document, go to the Place File-> ... As with any other image.

PS
If you have any doubts, you need to read - and understand - the difference between raster and vector.

Open InDesign and use the Import command.