Copyright itself is automatic and you own the rights of your photos, unless you:
... sign an agreement saying otherwise.
... are employed as a staff photographer, in which case the employer owns the rights.
... sell or give away your copyright ownership.
... are shooting under certain conditions in some countries.

Copyright REGISTRATION is a method of protecting your rights.

You already own the copyright of any photo you have taken (assuming none of the above) and if someone uses it without your permission, you can demand they stop using it and potentially go to small claims court to sue them for the market value of the usage.

Once copyright has been registered, if someone uses the photo without your permission you can demand they stop using it and go to federal court to sue them for the market value of the usage PLUS your legal costs PLUS various penalties (for example, a court can award up to $30,000 US per instance for deliberate removal of copyright protections, such as removing a watermark or deleting EXIF data).

Basically it comes down to is with unregistered work you're on your own, no legal assistance (unless you pay for it out of your pocket), you will need to pay any and all court costs, and at best will only require a minimal amount.

In contrast, a registered work can mean substantially larger sums of money awarded to you for infringement, you can likely get legal assistance and representation (very possibly on a contingency basis if you have a strong case where you don't have to pay upfront... your attorney gets paid by the infringing party via the court's award). The infringing party will also be responsible for paying any court costs you incur. This is all in addition to whatever the court decides to award you for usage AND to penalize the infringer.

There are several ways to register your copyright. You can load digital thumbnails onto a DVD or thumb drive. The last time I checked, it can be as many as you can fit onto the medium, possibly thousands of images, under a one-time registration fee. It also is possible to upload the image directly, but I believe there is a limit to the number of images (still, it's some hundreds of them IIRC).

To be fully protected... i.e., fully eligible for all the possible awards noted above... images MUST be registered 90 days or less after the date of first publication. Prolific photographers might just do a batch registration of their "keepers" four times a year. Others who shoot less might only need to do so annually but may want to prioritize any images that are published.

There is almost NEVER any good reason to sell or give away your copyright. Almost all legitimate usage can be handled through a LICENSING agreement.

In your case, you have been asked by an artist who wants to do a derivative work based upon one of your photos. You need to know what they intend to do with their painting, once it's completed. If they merely want to hang it on their own wall, display it in shows and don't anticipate selling their work, you might give them permission without any payment or for a $5 or $10 Starbucks gift card... or whatever seems fair to you. If they plan to sell the work you need to know what they will be charging and may need to adjust what they pay to license the usage. If they plan for their painting to be the basis for posters that will be sold in the tens or hundreds of thousands all over the world, you should be charging quite a bit more for the usage license (and they, in turn, should be licensing the usage of their painting with similar terms).

The license should be a written agreement between the two of you. It also can specify a length of time of the usage... starting and ending dates or X days or months or years from the date of the license. It also can restrict the distribution to a certain area such as a country or a region like "N. America"... or allow worldwide usage.

The license should state that it is single-use, or whatever you agree upon. And it should specify it's non-transferable, that they can't turn around and license usage of your image to someone else (this can occur... such as a news service that re-distributes images through its wire services). Finally, it should state that no transfer of ownership is intended or implied, that the copyright remains yours and any usage other than what's been specified requires a separate, written license and permission.

There are options under a license for you to give them exclusive usage for some period of time (probably not necessary here) and if you wish you can give the option of first right of renewal, possibly at a reduced fee (to encourage future business from them).

I ain't a lawyer, just a photographer who occasionally has to deal with these things. You may wish to consult a lawyer because there may be some other things for you to consider, perhaps due to where you live and work. There also are some books about licensing and pricing photos and photo services.

Copyright itself is automatic and you own the rights of your photos, unless you:
... sign an agreement saying otherwise.
... are employed as staff photographer, in which case the employer owns the rights.
... sell or give away your copyright ownership.
... are shooting under certain conditions in some countries.

Copyright REGISTRATION is a method of protecting your rights.

You already own the copyright of any photo you have taken (assuming none of the above) and if someone uses it without your permission, you can demand they stop using it and potentially go to small claims court to sue them for market value of the usage.

Once a copyright has been registered, if someone uses the photo without your permission you can demand they stop using it and go to federal court to sue them for market value of the usage PLUS your legal costs PLUS various penalties (for example, a court can award up to $30,000 US per instance for deliberate removal of copyright protections, such as removing a watermark or deleting EXIF data).

Basically it comes down to is with unregistered work you're on your own, no legal assistance (unless you pay for it out of your pocket), you will need to pay any and all court costs, and at best will only require a minimal amount.

In contrast a registered work can mean substantially larger sums of money awarded to you for infringement, you can likely get legal assistance and representation (very possibly on a contingency basis if you have a strong case where you don't have to pay up front... your attorney gets paid by the infringing party via the court's award). The infringing party will also be responsible for paying any court costs you incur. This is all in addition to whatever the court decides to award you for usage AND to penalize the infringer.

There are several ways to register your copyright. You can load digital thumbnails onto a DVD or thumb drive. Last time I checked, it can be as many as you can fit onto the medium, possibly thousands of images, under a one-time registration fee. It also is possible to upload the image directly, but I believe there is a limit to the number of images (still, it's some hundreds of them IIRC).

To be fully protected... i.e., fully eligible for all the possible awards noted above... images MUST be registered 90 days or less after the date of first publication. Prolific photographers might just do a batch registration of their "keepers" four times a year. Others who shoot less might only need to do so annually, but may want to prioritize any images that are published.

There is almost NEVER any good reason to sell or give away your copyright. Almost all legitimate usage can be handled through a LICENSING agreement.

In your case you have been asked by an artist who wants to do a derivative work based upon one of your photos. You need to know what they intend to do with their painting, once it's completed. If they merely want to hang it on their own wall, display in shows and don't anticipate selling their work, you might give them permission without any payment or for a $5 or $10 Starbucks gift card... or whatever seems fair to you. If they plan to sell the work you need to know what they will be charging and may need to adjust what they pay to license the usage. If they plan for their painting to be the basis for posters that will be sold in the tens or hundreds of thousands all over the world, you should be charging quite a bit more for the usage license (and they in turn should be licensing the usage of their painting with similar terms).

The license should be a written agreement between the two of you. It also can specify a length of time of the usage... starting and ending dates or X days or months or years from the date of the license. It also can restrict the distribution to a certain area such as a country or a region like "N. America"... or allow worldwide usage.

The license should state that it is single use, or whatever you agree upon. And it should specify it's non-transferable, that they can't turn around and license usage of your image to someone else (this can occur... such as a news service that re-distributes images through it's wire services). Finally, it should state that no transfer of ownership is intended or implied, that the copyright remains yours and any usage other than what's been specified requires a separate, written license and permission.

There are options under a license for you to give them exclusive usage for some period of time (probably not necessary here) and if you with you can give them option of first right of renewal, possibly at a reduced fee (to encourage future business from them).

I ain't a lawyer, just a photographer who occasionally has to deal with these things. You may wish to consult a lawyer because there may be some other things for you to consider, perhaps due to where you live and work. There also are some books about licensing and pricing photos and photo services.