No one really cares what kind of paper you use. What matters when extending an invitation is that you show that you really want the person to attend, and that the event is important enough that you have given it some thought, and gone to the appropriate amount of trouble. Formal written invitations are fine, but don’t waste time or money on the great engraved vs not engraved issues; do spend time on adding a personal note, indicating why the event will be more special to you if the invitee attends.
If someone goes to the trouble of issuing a social invitation (as opposed to a business invitation), you should go to the trouble of responding, in whatever format is appropriate. In most cases, you can just leave a voice mail indicating either that you would love to attend and look forward to it, or, that, alternatively, you appreciate the invitation but won’t be able to make it. No excuses are necessary, unless it is a close friend or family member who was expecting you to attend, in which case you should explain why you can’t. (Being shipped abroad, dinner with Tyra Banks, Sade concert, anniversary of your cat’s death, death defying secret mission, in training for Polar expedition, etc.). Telling white lies is okay, if you have to explain to your grumpy old aunt why you can’t attend her dinner party. But you must respond.
As in all things, a gentlemen does as he promises. If you have said you won’t be there, don’t be there. If you have said you will, do.