Why do you think that file size of 20 MB is not "good"? Is there some restriction on file size where you are going to print it?
The term, by the way, is not 'pixelized' but 'downsampled'. Downsampling does exactly what you are seeing: it makes the file smaller by cutting down the size of its largest parts: images. The only way to make an image smaller is to downsample.
Can I export it with best settings (at least 300ppi for printing) and not pixelized?
No, one rules out the other.
Apart from that:
If I export it with best settings it has a size of 20 MB, if I do it with lowest settings only
1,2 MB but it gets pixelized than.
You don't have to choose either of these extremes. There are lots of individual settings to fiddle with, so I suggest you go over all of them and manually adjust until the images downsample too much for your taste, or you have a file size you can live with.
And in doing so, always remember that you are JUDGING FROM YOUR SCREEN. A printed version is usually much sharper than what you can see on screen, so even if you think "well that ain't too bad", the printed version might look worse than you expected.
Thanks a lot for your answer The problem is that it's a presentation about my work for a company and the email attachment where I'm sending it too has to have a maximum size of 5 MB. That's really bad.
There are lots of individual settings to fiddle with, so I suggest you go over all of them and manually adjust until the images downsample too much for your taste, or you have a file size you can live with.
Well, I can only find some different Acrobat versions at export of Indesign and one like "smallest export" and one "highest quality". Where can I say, I want to keep it in 300ppi but resized for a smaller output?
Waht version of ID are you using? If CS5 or newer, Export to PDF (Print) instead of PDF (Interactive) and look at the compression tab in the export options. You can change the amount to downsample and change the qulity of the compression. For desktop printing, 100 ppi is probably adequate if you need to go that low, but 180 would be better.
Is this for a job application, or will they look at the material if you send them a link to a larger file instead of using an attachment? If they will, send the 20 mb version using YouSendIt or something similar.