I dont think you are talking from personal experience, but anyway.
When you grapple, you are working with the opponents weight and thats the different with the striking arts- your condition should be based on lots of lifting, controling and pulling of weights, close to your opponents body weight. The main reason why you gass, should be because you are not able to work with weights.
There is no serious competitor on high level, who wouldnt practice with weights.
The reason why you use oly lifts is because they are compound moves and include the entire body, which is more similar to grappling. You dont need to lift weights, close to the oly records, but enough to practice explosiveness during time, similar to 2-3 rounds of rolling. You can get injured with running as well, so if you really want to develop good condition, learn the lifts tech first and then you can blast away.
If you develop muscles, those muscles will be used to deal with the stress that you put them under, which is the main difference with bodybuilding.
Intervals and circuits are specific training, but thats why the TS is posting here, because he wants to know what is good for him to do. There are lots of those type of protocols in the sticky treads above.
10 minutes of tabata training with weights will do miracles for your cardio and also will burn a lot of fat
Magic 300:
25 pull ups
50 push ups
50 box jumps
50 deadlifts
50 russian twists
50 clean and press
25 pull ups
I do that in 16 minutes.