A lot depends on the addressing ie. you ISP may well provide you with two IP subnets and these are -
1) a /30 for the point to point connection to their router
2) a larger public IP range for your NAT use
if you connect the ASA directly then you use the /30 for the outside interface of your ASA and then use the additional range for whatever you need
if you connect to the router first then you use the /30 for outside interface of your router. Then you either need to -
a) use two of the IPs in the additional range for the ASA to internal router interface so you have already used some IPs
or
b) use a private IP address range between your ASA and the router but this can effect VPN termination on your ASA so it is often simpler to make sure you have a public IP on the outside interface of your ASA.
If the handoff is ethernet, which it is, then you can obviously connect directly to the ASA. Routers however have more functionality. You have already mentioned QOS but another potentially very useful feature is PBR which ASAs do not support.
With one ISP connection PBR is not an issue. But lets say you decided you wanted a second connection for backup or you wanted to use both links. Then PBR on the router is very useful and this type of scenario often comes up on these forums ie. ASA with multiple ISP links and the need for PBR to be able to use both links.
There is no "correct" answer to this. If you are not planning on a second link and you do need any of the features a router could give you then it can be an additional cost you don't need and you can simply connect directly into the ASA.
Jon
