Resistance Training

I signed up a while back for 10 sessions with a private trainer at the gym downstairs from where I work. I'm nearing the end--it was interrupted for a number of weeks when neither the trainer nor I could make appointments.

Historically, I've relied on martial arts, some running (nowadays elliptical machines) and some body-weight resistance training--push-ups, squats, etc.--to get into shape.

My trainer says that running alone can eat into muscle, and that you need resistance training--weights, Nautilus-type machines--to get into the best shape (along with cardio work like running).

One of my favorite exercise books, The Ultimate Boxer, says that weight training is beneficial for those martial artists known as boxers--but that if you're limited in time, you can get great benefit from push-ups, crunches, etc. instead.

I wonder, to really get into and stay in shape, what do you add to martial arts? Running? Sprints? Calisthenics-style resistance training? Weights?

Don't tell my plyometrics, my knees and feet can't take those!