I want to set up a hardware (router) based VPN at the lab and at home (plus my Android phone).
What do I need?
I know I could just get any of the dozen software based VPN's that are advertised constantly, but I think that having hardware just do it at the router level is way cooler.
I presume my phone will need one of those software options though.
My home router supports OpenVPN and PPTP
My lab router is an old TP-Link C1200 and Google Gemini seems to think it's capable using OpenVPN via tplinkwifi.net ? 
I also have my dedicated server in the US, so can potentially set up a VPN via that server box I presume?
Dave, I would stay away from any of SOHO routers as front end to the Internet.
The AX6000 from TP-LINK may be a good AP choice at home, but I wouldn’t trust it as a router,
the AX6000 can be configured as AP only and link with decent router.
You should check pFsesnse and OPNsense. I didn’t try OPNsense, but I used pFsense since ~2011 as firewall for >10 mln users
(in peak hours > 3Gbs traffic), vpn p-2-p solution and as vpn server for warrior admin users.
Both solutions offer IP layer 2 routing and filtering.
As VPN protocol I suggest OpenVPN, or WireGuard.
Using pFsense, or OPNsense you could link all your locations over p-2-p of your choice
and access it from any place in the world using an vpn client.
pFsense (aka Netgates and formerly Electric Sheep Fencing, LLC) is offering appliances,
but the software is free and you could build your own using older, decommissioned hardware.
Link to pFsense:
https://www.pfsense.org/Link to OPNsense:
https://opnsense.org/Both are based on FreeBSD which in my opinion is best when come to IP protocol.