Cape Cod Massachusetts USA
Pretty much everyone here has asked that question at one time or another. Copyrighting a work in the US copyright office is certainly an option for you. If you opt to do so, then you'll most likely compile a group of poems to submit together - in which case, your poems would not be listed individually - The name of your "volume" would be listed. If you submit each one separately, it can certainly get costly.
Notice that each poem posted on this site has a "copyright" notation at the bottom of the screen when it is viewed. In reality, every poem posted is time-dated. If there were ever a discrepancy about who wrote a particular poem, your proof would lie in the "earliest" posting date. Your best protection, then, is to be sure that YOU are the first person to post your own work. Protecting you and your rights to your own work is a primary concern for Ron and everyone who helps keep this site running smoothly. You'll always be protected here.
As for posting on your own site, the same guidelines would follow. There is always a record of dates and times that transfers are made... Just make sure that you have access to that record, and you should be fine.
Perhaps others will have more to offer on this subject??