When entering text, make sure you have anti-aliasing turned on. Always make the image at the size you want. Better to reduce image than try to enlarge it as you may have a pixelation problem.
Vector graphics is fine only if you are going to be resizing the image a lot. It DOES make a nice image, but most web formats, other than vectored images, are more popular. GIF/PNG is good for small images like buttons. They support transparency.
Larger images of good quality should stick with the jpg format and compressed for web use to keep file size down.
The program (Corel) is a very good graphics editor so any problems are in the making of the image.
Could try these if you think not.
FREE software:
http://www.gimp.org/downloads/ (Animation included)
http://www.blender.org/download/get-blender/ (Animation included)
Blender for Dummies (PDF) Download: http://www.baydownloads.com/search.php?a=4megaupload&q=blender%20for%20dummies%20pdf
UnFreeze: http://www.whitsoftdev.com/unfreez/ (Animation)
FREE software (No Animation):
http://www.getpaint.net/ (Very user friendly)
http://www.inkscape.org/download/ (Very good for vectored graphics)
http://www.download.com/PhotoScape/3000-2192_4-10703122.html?tag=mncol
http://www.online-image-editor.com/