Actually, you'll have to parallel to the one line that's connected, the second set of connections is really for the second phone number and line.
Since you're running wires, I suggest the following wiring for the modem.
Purchase a DSL splitter and install it at the telco NID (Network Interface Device). This is the place the telephone lines come into your home wiring, usually either in the basement or outside near the other utilitiy connections. Run a direct line from the DSL port on the splitter directly to the DSL modem. Connect all of the other phone instruments to the telephone output of the DSL splitter. All of the DSL analog side wiring should be CAT3 or better twisted pair from the telco service entrance to the DSL/ADSL modem. You can use one of the twisted pairs in CAT5 cable if you have that on hand. The splitter I've used in the past is the
Wilcom PS-36, it's good for any DSL/ADSL service worldwide.
This is as good as it gets for DSL installations, and will usually solve in-house wiring issues.