Postal services tend to be really nasty about use of postal code data so getting a hold of that postal code data will probably be quite difficult or expensive, and you'll probably get in trouble if you try to publish/distribute it. The rest of the data should be easy to get from a source like OpenStreetMap or Natural Earth depending on your particular license requirements. Don't simply trace over an existing map unless you have explicit confirmation that it is public domain, or has been licensed to you under terms suitable for what you are doing.

Generally, to work with real world map data, you need a GIS rather than graphics software. Once you have it in the form you want, you then export to an image and can finish up with graphics software if necessary. There isn't really a way to make such software "easy" without making it so restricted as to be near useless.