When to use routers and when to use layer 3 switches
Solution 1:
As you already know, a layer 3 switch includes a basic router. If the device has the functionality you need, then it should be fine to use. For instance, a layer 3 switch generally won't do NAT or have ports suitable for connection to a WAN. But it sounds like you will not need either of those.
Solution 2:
Whats the nature of the traffic ?
Gigabits of line-rate traffic with lots of frames/packets/bytes with quite simple ACLs? Then you want L3 switching.
Or lots of ACLs, Megabits/sec of traffic, with possible shaping, policing, or NAT ? Are there VPNs to be terminated? Then you want a router.
Ideally your network would have a L3 switch internally for fast traffic, and the router would sit between the core and the internet and any remote sites.
If you want it all in one device for simplicity, then your network design might need revising, so its time to call in a consultant with some external viewpoints, or consult an IT expert you trust.