Do I need to put a public IP on the spare MX - configured locally, and then add that in IP in via dashboard?
Configure IP before plugging in, also use virtual IP as you should have enough to share one between the MX pair.
I can't find a way to put an inside IP on the spare MX250 via the local dashboard?
Does VRRP handle the LAN side? Meaning I don't add an IP on the LAN interface of the spare MX250 at all?
The LAN interface shares the IP, it uses VRRP so you don't need to add an IP here. Note if connecting to a switch stack or hsrp/vrrp pair, you should have one link from each MX to each switch.
Should I leave the LAN interface shutdown until it's added in via the Configure warm spare button? (like willette suggests)
Configure warm spare should be done before connecting the warm spare MX but ideally after upgrading it to the same firmware. You can do this by adding it to a test network first, then removing that network and adding as warm-spare
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