What's involved in making wedding invitations -- are you printing them, storing inventory, inviting clients into your home to view samples? Anything that could increase the landlord's liability (e.g., increased foot traffic in and out of the building) could become problematic.
Similarly, if you own a house, are there any zoning ordinances that would prevent your running a home-based business? Local government officials may not bother a solopreneur tapping away at her computer, but any more activity than that may draw attention.
Another issue will be your business name. Generally, activities in the realm of "creative services" don't require a "license" -- such as the way plumbers need to be licensed or lawyers need to be licensed to show a degree of educational proficiency in their profession. That said, if you are engaging in business using any kind of trade name (such as "Susan Smith Graphic Design") beyond your given name, you'll need to file a certificate with your local county clerk.
But the inquiry doesn't stop there. Just having a trade name does not protect you from personal liability. As a result, you may want to form a business entity such as a corporation or limited liability company. You will want to speak to a local business attorney and accountant to decide which form is best for you.
Finally, like any other business, you have the issue of how to set appropriate expectations with your clients. Also, being in the creative services field, you may run into intellectual property issues. These can be covered with a well-worded contract that accurately reflects how you wish to do business with your clients. A local business attorney who understands your industry can help you create an agreement for you with standard terms that actually apply to your business.
Related: Business Licenses and Permits
Related: How to Bring Business into Your Home
Related: 10 Ways to Grow Your Home Based Business