In production right now, are the Piper PA-28-181 Warrior, the French Robin DR400 of which several versions are available and for sure, the Austrian built Diamond DA20 Katana. There are several aircrafts certified in lighter classes which work there as trainers as well.
The Katana has the advantage of the fuel economic Rotax engine and will make up the training considerably cheaper than older designs.
The Warrior and the Robins are 3 to 4 seaters, a little more expensive but the pilot can take passengers along right after the exam without the need to transition to another plane.
I trained many pilots on the PA-28's, like them very much and can recommend the plane. Anyhow, my real favorites as trainers are the French Robin and the Swiss AS202 Bravo (out of production for a while) as both of them are real nice in the controls. The Bravo even allows some aerobatics, so spins in the training can be done.