It'll do just fine. Overkill is a matter of opinion.
You want a rule allowing access from LAN net to "any" not the gateway IP.
Of course, you want to block access from LAN to anything you don't want your guests to have access to.
Having access to free software like pfSense, I can't imagine why anyone would want to run the "firewall" built into a DSL modem, but that too is probably a matter of opinion.
Sorry for the noobness, but I'm trying and the documentation references here are minimal, most to buy the book if you want anything detailed(which I don't like)…
Hmm. There are plenty of Captive Portal setup walkthroughs available. From what you've described so far, it's a simple firewall rule problem.
https://doc.pfsense.org/index.php/Captive_Portal_Troubleshooting
doc.pfsense.org. Charge: $0.00