Yes, you can, you don't need anything other than the words
EXPERIMENTAL to be visible by the passenger. Your PPL is fine for flying experimentals, although like any other aircraft change, I would get instruction from an experienced instructor in that type/model before going solo. Experimental aircraft can have some pretty different handling characteristics.
So, from a regulations standpoint, you are looking for CFR 91.319: Aircraft having experimental certificates: Operating limitations.. According to (j) of that:
No person may operate an aircraft that has an experimental certificate under § 61.113(i) of this chapter unless the aircraft is carrying not more than 6 occupants.
So you can have up to 6 occupants (including the pilot).
Do I need something special if I wanted to buy one of these planes?
No, your PPL allows you to fly experimentals, but as I said above, please get training from an instructor familiar with the aircraft and its handling characteristics. Many dear departed pilots probably wished in the last moments that they had some formal training in the experimentals they bought. You should also get somebody to go over the aircraft mechanically that is familiar with that model. Also look into your insurance costs, the airplane may be cheaper, but your insurance will probably be more expensive.