Its a good idea to stay away from weights if you are preparing for BJJ. strength is not something you will be cultivating in the beginning although it will feel like it. The goal will be in fact the opposite , using as little strength as possible.
There is no way i know of to prepare your cardio for ground fighting other than ground fighting, running is good, any stand up stuff is fine but will never really work your cardio the same as when you actually wrestle. Look to cardio training from wrestling they have many excellent drills and tricks.
Each phase of combat has its own unique cardio, each is slightly different in its effect so that good cardio in kickboxing will not always translate to good cardio on the ground or in the clinch. Likewise good ground cardio will not translate to standup or clinch. You use a different muscle set in each phase.
Do lots of situps, pushups is great, squats, jumping jacks, running in place.
A great body weight conditioning site is
Scrappers Body Weight Training its great stuff.