I'm new to Buddhism, and I have some trouble understanding some core aspects on meditation. Is Anapanasati considered Samatha or Vipassana?
This is my personal opinion. If you concertate of on the flow of air over the sensation (you sense the flow from the touch sensation) a conceptual image of the the air flowing will form in your mind. This way you can get to Samatha. If your focus is more of the fleshy part and the sensation of the body and air this is more tilted towards Vipassana. In either case both develops to some extent. Pure Samatha you can just be mindful of the flow of air as an body of air that goes in and out. As an alternative it is not necessary to look at sensation to make the Vipassana tilt. You can look at the process (in & out) itself. In this method when you progress you start seeing a process of expansion and contraction. Some lineages advice to look around the stomach but it is not necessary. You can experience the expansion and contraction on the sides of your nose or in the whole body it self or part of the body you look at. (This effect happens when you do Kayanupassana also.)
Main thing is that you should actively be conscious of the start to the end. Be mindful of the length. When the breath starts be very alert. After some time our breath will quickly show down and stop. Then if you keep your stillness of your mind and sharpen your senses you see it has not actually stopped, but jut got finer. Sometimes you can move your attention to you chest area or stomach (do not jump too much or you will loose your stillness). Like vice this cycle goes for some time until it it does actually stop and there is no movement in the body.
Doing the in breath be mindful of the start middle and end of the in and out breath. Each instance be actively mindful of what stage you are in. At the end of the in or out breath evaluate if your mind wondered away. Do this until it becomes second nature to you and you do not actively have to do it any more. If you breath has stopped just be alert and you will start seeing some movement some where again. Repeat until it actually stops. In between you will feel some lightness and pleasantness in your body and at some point it also will disappear into subtle vibration which is very hard to see.
Best is to do it will the Vipassana slant so you develop both. If you do the other and get used to it it might be difficult to change later on.
Also be warned this this is more of my opinion and understanding.
Some related answers:
What is the Interpretation of Parimukham in the context of Buddhist Meditation?
It depends on how it is practiced. According to the tradition of the commentaries(I think it comes from the commentary on the Kattavathu, the fith book of Abhidhamma but I'm not totally sure), the distinction between samatha and vipassana meditation lies in what the object of meditation is. In this model, meditation on an object of ultimate reality (that is to say, meditating on that which is experienced directly such as sensations, feelings, etc...) is considered vipassana, and meditating on an abscract concept that is more than just direct experience is samatha.