There are two common types of ASIC miners, those that can mine SHA based coins like the Antminer S9 and those that mine Scrypt hashing algorithm based coins (see Antminer L3+).
You can determine what type of coins your ASIC unit can mine by checking the algorithm that the coin is based on. If it is an SHA-256 based coin then you will be able to mine it on an ASIC made for Bitcoin such as the Antminer S9 or Antminer S7. If the cryptocurrency is a Scrypt coin such as Litecoin then it can be mined on Scrypt based ASICs such as the Antminer L3+.
Newer ASIC hardware which was released in 2017 specializes in other hashing algorithms such as the X11, Qark and Qubit. The Antminer D3 for example, mines coins based on the X11 hashing algorithm.
Once you determine what type of coin you are interested in mining, narrow down your hardware options by finding the ASIC for your coin’s hashing algorithm (i.e SHA, X11, Scrypt). Then, spend some time looking through reviews of the hardware to figure out which ASIC will provide the quickest ROI. You can also consider what coins share the same hashing algorithm as they will be your alternatives if you choose to mine a different coin along the way.