Samatha meditation is concentration meditation, where the mind is focused on a single object, usually the breath, until a unity of focus has been established. This is sometimes called Jhana.
Vipassana meditation is insight meditation, where the mind is directed to experienced phenomena such as thoughts or sensations in order to see them clearly as impermanent, dissatisfying, and non-self.
In some traditions, such as the Goenka or Mahasi traditions, "dry" vipassana, where there is very little pure concentration meditation, is supported. However, in practice, a great amount of concentration is developed through insight.
In others, like Buddhadasa or Ajahn Chah, essentially do not separate them at all and say that the cultivation of concentration and Jhana leads to insight.
It all depends on what tradition you're interested in. I would personally recommend taking a while to focus on developing concentration through annapanna, or breath awareness. Try and find the point where you most distinctly feel the in and out breath, and then establish your mind on that point like a gatekeeper; don't follow the breath in or out, just note when it hits that one spot and when it doesn't. When your mind wanders, bring it back. Try and "know the breath," understanding directly the length, duration, intensity, etc. that each in and out breath has. Don't think about it analytically, saying, "That was a short breath, I bet the next one will be longer!" Just know it directly. That might sound weird, but you'll soon grow to see the difference between knowing at the experiential level and just thinking. Try and examine each breath to see it as impermanent and out of your control. Try and keep focused and calm your mind, but when other thoughts invade, just note how impermanent and uncontrollable they are as well. Do that for a while, establishing concentration and mindfulness until you begin to become more and more fixed on the breath at that one single point of entry.
In the suttas, the Buddha never says, "Do samatha" or "Do vipassana." He just says "Go meditate." In truth, you can't have samatha (concentration) without vipassana (insight), or vice versa. Like a bird with an injured wing, having only one side developed will hamper you. Instead, they should develop together. So don't worry too much about whether or not you're doing samatha or vipassana; the important thing is to sit and be mindful!
But I'm no meditation master! Other people will have other ideas. This is just what I would say off the cuff. Good luck and welcome to the Sangha!
Gain and loss, status and disgrace,
censure and praise, pleasure and pain:
these conditions among human beings are inconstant,
impermanent, subject to change.
Knowing this, the wise person, mindful,
ponders these changing conditions.
Desirable things don’t charm the mind,
undesirable ones bring no resistance.
His welcoming and rebelling are scattered,
gone to their end,
do not exist.
- Lokavipatti Sutta