The way I’d configure the MX is with the P2P on one of the LAN ports, as an access port in its own VLAN so it essentially becomes a Layer 3 link. Then configure a static route to the subnets at the other site with ‘while next hop responds to ping’ (or ‘while a host responds to ping’ if you prefer) pointing across the link. The Static route will have preference over any VPN routes so the traffic will go over the P2P link.
If the link fails then the Static route will drop out of the routing table and the VPN route will become active, sending the traffic back over the VPN link.
You won’t be able to use the point to point link for Internet traffic as you can’t set a default in the event that the Internet fails, that’s not the way the MXs work. As such you should never end up in the situation where internet traffic goes across the P2P link, unless you purposely put in a default route to do that (which means nothing will ever go out the internet links, except traffic to the Meraki cloud).
Re: Best Config for new point to point branch to head office link
Just to add to what Bruce said: make sure you configure the Ping-checks on both ends. Both sides must use the p2p link *or* the s2s-vpn. Otherwise you get asymetric routing and the traffic will be dropped.
Another possibility: If your internal switches support these connectivity-checks or a dynamic routing-protocol *and* you don't need any filtering between the sites, then you can terminate the L2-link on an internal switch.