Whoever that guy is, he’s wrong. 300dpi is indeed bottom of the barrel in terms of print ready resolution, but that’s like saying a Ferrari Enzo is slower than a La Ferrari. 300DPI will most definitely get the job done and well.
The issue is VERY likely on your end (no offense). Either by way of paper choice, print settings, actual printer quality, inks used (cheap china crap, versus OEM), resolution of the actual logos within the file itself, etc.
What do you mean when you say that you can’t set the document size properly? Simply create a new document, adjust both the resolution and page size within the document setup window that apprears (you may need to manually define the dimensions if there’s no preset for A3), then hit go.
As far as finding and using high resolution logos, get yourself vector drawn versions whenever and wherever possible. Many are available here on the site. They’re effectively infinite resolution. Simply placing them into your raster document (Photoshop, Gimp, etc.) will afford you the ability to scale them as much as you’d like without compromising the quality, no matter what the document resolution is set to.
