Exporting Art from CorelDraw X4

I create various objects in CD X4 and have a dickens of a time exporting them as clean graphics.  My printer does not use CD, and I don't use Illustrator and am looking for a format that will fall in between both.

Let me create a scenario.  I made a sign in CD, with a background color, text, and a photo.  I want to save it in a middle ground format like PNG, but that option is not available to me in CD.  So what I have tried is to copy the image and paste it in Paint Shop Pro, my preferred image editing program (one owned by Corel, I might add) and I can save in PNG in that program...but the images are pixelilated and look horrible. 

I also created my logo in CD and did the same for my website, and it doesn't look so hot.

How do I perform these tasks, hopefully using the software I already own?

Thanks.