I would say play Demon's Souls first as the game is getting older and by the time you finish Dark Souls, play a pallet cleanser, and then get back to it the multiplayer population may have decreased or Atlus may have shut down the multiplayer server. It was recently reinvigorated because Demon's Souls was released on PSN 2 months ago. It is $20, FYI PSN currently has a promotion, for every $50 you spend in March, you get $10 added back to your wallet in April.
By the time you are ready to play Dark Souls an ultimate edition with the story DLC included at a reduced price may be available to purchase on PSN.