A written agreement over email could secure you certain non-exclusive rights, but if you want actual rights to using the image in anyway, including deriving from it for marketing purposes or adding text to it for a cover, you should secure a contract and make some sort of payment in order to create an additional paper trail.
As is the case with any intellectual property, you need to purchase rights from the copyright holder. Unless the rights have already been sold, you'll be purchasing them from the artist who created the piece.
You will either be buying
exclusive rights or
non-exclusive rights.
Exclusive means you are
the only owner of the rights purchased, and
non-exclusive means that others will be
sharing those rights with you. The use of stock images from mega stock websites (something I don't use unless requested by the client) is sold en masse under non-exclusive rights. If you're working with an artist, and the individual is only offering non-exclusive rights to you, you may want to inquire about who else is or might be purchasing these rights as well.
Something many new freelance graphic designers miss doing is providing information about the copyright of stock to their clients, which puts the client at risk since mass distributed stock can be suspect of origin and is released under a non-exclusive contract that needs to be kept in your records.
If there is a real person's face in the image that you are purchasing, you will want a copy of the model release form, because the creator of a photo of a person is
both the photographer
and the model. Their are also privacy issues in play for that one.
You'll probably be going the exclusive route when working with a commissioned artist. You'll need to decide what rights you'll specifically be purchasing. And the price of the work will probably differ based on what rights are for sale.
In the US, the rights that are up for negotiation are listed in Sec. 106 of the US Copyright Act of 1976.
Sect. 106. Exclusive rights in copyrighted works
Subject to sections 107 through 120 [17 USCS Sects. 107-120], the owner of copyright under this title [17 USCS Sects. 101 et seq.] has the exclusive rights to do and to authorize any of the following:
(1) to reproduce the copyrighted work in copies or phonorecords;
(2) to prepare derivative works based upon the copyrighted work;
(3) to distribute copies or phonorecords of the copyrighted work to the public by sale or other transfer of ownership, or by rental, lease, or lending;
(4) in the case of literary, musical, dramatic, and choreographic works, pantomimes, and motion pictures and other audiovisual works, to perform the copyrighted work publicly; and
(5) in the case of literary, musical, dramatic, and choreographic works, pantomimes, and pictorial, graphic, or sculptural works, including the individual images of a motion picture or other audiovisual work, to display the copyrighted work publicly.