Is there any simple way to know when to choose which SSH Key- type, rsa, dsa, ecdsa?

Among the SSH key types, in practice the RSA key will work everywhere. ECDSA support is newer, so some old clients or servers may have trouble with ECDSA keys. A DSA key used to work everywhere, as per the SSH standard (RFC 4251 and subsequent), but this changed recently: OpenSSH 7.0 and higher no longer accept DSA keys by default. ECDSA is computationally lighter, but you'll need a really small client or server (say 50 MHz embedded ARM processor) to notice the difference.

Right now, there is no security-related reason to prefer one type over any other, assuming large enough keys (2048 bits for RSA or DSA, 256 bits for ECDSA); key size is specified with the -b parameter. However, some ssh-keygen versions may reject DSA keys of size other than 1024 bits, which is currently unbroken, but arguably not as robust as could be wished for. So, if you indulge in some slight paranoia, you might prefer RSA. To sum up, do ssh-keygen -t rsa -b 2048 and you will be happy.