So you're sending ASA data to Splunk using ASA SYSLOG feature.
I assume this means its using UDP port 512.
So now you would configure your UDP port 512 input on your forwarder or indexer. Note if you're using linux and followed best practices and installed splunk as a non-privileged user (didnt install as root) then splunk will not be able to bind to ports lower than 1024. That's a linux only security feature.
As for what sourcetype to use, cisco:asa seems the most appropriate but it all depends on what your cisco team is doing related to logging practices. If they're using out of box logging configs... cisco:asa should be fine. If they're using custom logging settings, you might have to create your own sourcetype, but you'll still probably be best starting with the cisco:asa and then modifying and using the data preview.