Specter can be configured to connect to the bitcoin network via Bitcoin Core - this is the default option and is the least demanding on your server. This is the correct choice if you are running a Server Lite. However it will be very slow to rescan after adding a new wallet. Electrs can be used instead which will be far faster, but is not advisible if you are running less powerful hardware, or pruning in Bitcoin Core.
If you would like to know how to use a signing device with Specter please see see our documentation here
If you'd like to use your own Mempool to open links in Specter head to "Settings" -> "Block Explorer URL" and input either the .local or .onion address of your Mempool service.