How can I set up an Apple TV (4th gen) connection to a PPTP/L2TP VPN?
One way to do this is to use a router or Mac to connect to the VPN and then share that connection with the Apple TV.

Below is one example of how you could do this using a Mac. This should also give you the basic idea if you need to do something similar with a Windows machine or router1.

Share VPN from a Mac


Connect your Mac to the internet via ethernet cable (i.e. connect it to a router, modem, etc via ethernet)
Set up your VPN connection in System Preferences > Network (obviously you'll need the address and authentication details to do this)
Click on the Advanced... button
Ensure you tick the Send all traffic over VPN connection checkbox
You will also want to make sure that the two Disconnect options are not enabled
Click OK
Ensure you also tick the checkbox for Show VPN status in menu bar
Now go to System Preferences > Sharing
Highlight (but do not tick) the Internet Sharing service in the lefthand pane
On the righthand side, select the VPN connection you created at Step 2 from the Share your connection from drop-down menu
Now select the Wi-Fi port (i.e. tick the checkbox)
Click on the Wi-Fi Options... button
Give your new Wi-Fi network a name, password etc
Click OK
Now tick the Internet Sharing service in the lefthand pane


1 It's impossible to give you precise steps as routers vary significantly. However you would need to ensure your router is capable of doing this and will need to refer to its user guide.

NOTES: 


You can also share a Wi-Fi connection via ethernet (although I suspect that's not practical in the case of a Mac > Apple TV.
If you can't connect your Mac to a router/modem via ethernet at Step 1, you could use a Ethernet to Wireless adapter instead. This just means the adapter is connecting to your usual Wi-Fi network and that you're connecting your Mac to the adapter via Ethernet.
Since you want this to be an always on connection, it'd mean your Mac will need to always remain on. It's also why Step 5 above is important. You may also need to adjust your System Preferences > Energy Saver settings.


Now, whenever your Mac is connected to the VPN, it will share the connection via Wi-Fi. This means you can connect any device to the new Wi-Fi network you created at Step 13 (such as your Apple TV). 

Using the VPN connection

To make this work with your Apple TV:


On the Mac, click on the new VPN Status icon in the menu bar
Select the Connect option pertaining to the VPN connection created previously
Once the connection is established, your Wi-Fi icon in the menu bar will change to indicate your Mac is now sharing the VPN via Wi-Fi
Now go to your Apple TV and connect it to this Wi-Fi network