Exercises to do
You should develop the primary physical attributes for combat sports: strength, power, mobility, conditioning. This will involve learning: you should not restrict yourself to exercises which "can be done alone by someone with no or little experience".
(Much of this answer is cribbed from my answer to a similar question.)
Therefore, you'll want to first develop an aerobic base, best developed by running, swimming, rowing, or biking over medium-long distances. That could mean getting a solid mile or 5k time, or rowing 2000 meters on a machine. You'll want to train basic prerequisites for strength training: push-ups, pull-ups, dips, air squats. You'll also make sure that you've got the necessary mobility for rigorous training, like an effortless third-world squat, front rack position, and good posture. If you're not fit, I'd recommend the training program in Robb Wolf's book, The Paleo Solution (which is mostly about diet, but has a very respectable ramp-up program for physical training).
Once these basics are in place, the more important strength training can begin: barbell squats, deadlifts, bench and overhead presses, power cleans. The book Starting Strength by Mark Rippetoe and Lon Kilgore is a great choice at this point. You'll still work on conditioning and bodyweight stuff during this time, but the priority should be resistance training. The medium-distance runs would become less frequent, the bodyweight work relegated to warm-up or accessory exercises at the end of a workout. Short, high intensity conditioning work such as kettlebell, dumbbell, or barbell complexes, sled drags and Prowler pushes, sprints and hill sprints would fit in a few times a week after you've developed a reasonable level of strength--a dozen pull-ups, a bodyweight squat for reps, a greater than bodyweight deadlift. Setting goals like a double bodyweight squat or deadlift, or a bodyweight press, are helpful in spurring progress as long as they don't cause you to overlook injuries or mobility problems.
Eventually you'll want to add power development work to your strength training. Exercises would include snatches, jerks, push presses, broad jumps, height jumps, and increasing the priority of power cleans. Benchmarks such as a bodyweight clean-and-jerk or being able to jump up to sternum height are useful goals.
At that point I'd also consider gymnastic work: work yourself up to a pistol (and then jumping or weighted pistols), front and back levers on rings or a bar, muscle-ups, backflips, and so on. These feats build on your strength base and develop other attributes like balance, proprioception, and coordination. They're also clearly impressive.
This training would take several months to several years, and would well prepare you for technique training and sparring once you have the chance.
Exercises to Avoid
Do not engage in bodybuilding, because it has goals contrary to the goals of athletics. Avoid excessive long-distance running; as Forrest Morgan notes in Living the Martial Way, long, slow, plodding exercise makes for long, slow, plodding fighters.
In fact, don't get too hung up on any one activity: combat sports and martial arts are best performed by people who are athletic across essentially all disciplines. Those who specialize in strength, or mobility, or cardio, or any other attribute all suffer because opponents can exploit the inevitable areas where the specialist is deficient. A combination of gymnastics, Olympic lifting (accompanied by the attendant strength training), and various forms of cardio and locomotion is generally ideal for general purposes and preparation for martial arts.
