Part of being a pagan is building a relationship with your gods. Worship of the gods is the main focus of paganism, and it is this spiritual connection that makes a pagan truly a pagan. Without a focus on deity and spirituality, paganism would just be a form of sorcery or magecraft. And while there is nothing wrong with sorcery and magecraft (I've known a few Chaos Mages), those of us who wish for a more spiritual connection with the Earth may find that looking towards ancient beliefs helps strengthen our connection with the Earth and each other.
Pagans draw their deities from ancient mythologies. Many Wiccans simply follow the Mother Goddess and Father God/Horned God, twin deities of nature. Some Wiccans give these deities names from mythology, others simply call them the Lord and Lady. Other pagans are polytheistic as opposed to duotheistic, and worship many gods. One friend of mine follows Asartu, the reconstruction of the Old Norse religion, as so worships the many gods of the Norse Pantheon.
When choosing your deities, there are basically two paths to follow. The first is to do research on the deities of your ancestral region. if you're greek, being a Hellenistic pagan may work for you. If you're Irish, you may choose to worship the Tuatha De Danann. This gives the worship of your particular deities a personal touch.
But what if you aren't of European descent, or don't feel a particular tie to your ancestors? I hold that is completely valid to worship a pantheon you hold no biological connection to, but that speaks to you personally. If there is a particular mythos that captures your imagination, go for it! I see no reason pagans should restrict culture on ethnic grounds, considering most of us are white.
One important note, though, is that you should try not to appropriate religious deities of cultures that have been historically repressed. While it is true that paganism was, until recently, looked upon with suspicion and repressed, this cannot be compared to the genocide that has befallen people of color around the world. So if you're not of Roma descent, don't go around appropriating Roma practices, for instance.
Whatever deities you choose, be sure to do some research on them so that you know a bit about what panthoen you are choosing. Remember, the point is to build a rapport with your gods, a working relationship of reverence. It is not a transactional relationship, but one of mutual love and respect.
For myself, my background is primarily in Wicca, but I am of Italian descent on my father's side. So I worship the God and Goddess, but have been considering identifying them in more concrete form as two Roman deities: Diana and Janus. These two deities have uniquely Roman origins, and thus they feel authentically Italian to me.
Diana has been Hellenized and associated with Aretmis, but she actually had a separate origin in Italy as Diana Nemorensis (Diana of the Wood). Her sanctuary was at the Lake of Neimi, and was originally a grove with a cult image as opposed to a whole temple. The cult image depicted her as a threefold goddess, associating her with the moon an the hunt, motherhood, and the underworld and magic.
Janus, on the other hand, is a deity that was never Hellenized. He was associated with beginnings and endings, as well as doors, passageways, and the sun. He is also listed as one of the names of the father god in The Book of the Holy Strega by Raven Grimassi, although the authenticity of Grimassi's work has been called into question. Janus is often depicted as having two faces, to show his nature as the god of beginnings and endings.
Diana as the moon goddess and goddess of magic fits nicely with the Wiccan belief, and it is even believed that her cult may be the source of the original mother goddess. Some scholars have refered to the witch cult in Europe as a Dianic cult, for instance. As for Janus, the notion of beginnings and endings fits nicely with the theme of the wheel of the year. But I also fondly remember a book from my childhood in which a double-faced coin with an image of janus on the front and keys on the back served as the door between worlds, allowing a young boy to travel back in time. That book was The Castle in the Attic by Elizabeth Winthrop, and it was a favorite of mine. So worshiping Janus also plays into my childhood memories, and the themes of fantasy and traveling between worlds that are frequently featured in my writing. It adds a nice personal touch to my pagan practice, and helps me to feel rooted in my beliefs.
All in all, I encourage you to find the gods and goddesses that speak to you on a personal level and begin forming a relationship with them, no matter who they en up being. Developing a relationship with the gods can be one of the most rewarding parts of pagan practice.