Common noob mistakes:
Cooking things too long. Meat dries out when it's cooked to too high an internal temperature. That's the whole thing, and it's true no matter how you cook something. If you like your meat to be completely devoid of pink inside, it will be dry. No avoiding it. Find out what's a good temperature for the doneness you desire, and use an instant-read thermometer to find out when you get there. You will also find that some cuts of meat want more cooking than others. A skirt steak wants hardly any cooking because it dries out easily. A New York strip, with good fat marbling, can withstand more cooking because it has that nice fat to keep things moist.
Cooking with too much heat or too little. When the heat's too high, you burn the outside before the middle can get to the temperature you want. If it's too low, you never really get a good sear on the outside, and miss out on much of the grilled food experience. And you'll need to learn to tailor your heat to the needs of what you're cooking--fish typically needs less than chicken, which needs less than beef or lamb.
Putting the meat on too early. You need to wait for the charcoal to ash over and stop flaming. If you don't wait for the coals to get right, you run a much greater risk of flare-ups and scorched food, not to mention off flavors from unburned wood or fillers in your charcoal. This is a non-issue with gas grills.
Not preheating the grate. You need to put the grill grate over the coals as soon as you can so it preheats well. If your grate isn't preheated, you won't get grill marks, and your meat is more likely to stick. You need to do this if you have a gas grill too--maybe more so, since they typically don't get as hot.
I'd recommend that you find a basic book about grilling. Any of Steven Raichlen's books will give you the general tips on how to do things. I'm not wild about his overuse of rubs and sauces--I think they're totally unnecessary most of the time--but he does know his way around a fire and a grill grate.
However, if you want your meat well-done, be prepared to eat a lot of dry (and likely tough) meat. Your only option at that point is to switch to low-and-slow techniques that cook things like pork shoulder for a really long time at a low temperature (traditional barbecue). The meat gets fully cooked, but because it has a lot of fat and connective tissue to render, retains a moist mouthfeel. But this isn't grilling, per se, and takes many hours.
I have neither cooked nor eaten kangaroo, but I think the information that it is very lean should be sufficient to answer this question. Smoking is a low and slow technique that is used to make tough cuts of meat tender. This works by using a low temperature to break down the tough connective tissues which makes the end result both tender and moist. This would not work with a lean cut of meat like a filet. You'd just end up with a tough piece of meat. So unless you really go after the toughest bits of the 'roo, I'd advise against smoking.
As ESultanik says in a comment, to attack the lean parts of the animal, treat it like any other piece of non-fatty meat (filet / tenderloin for example). Use a very hot grill and shoot for an internal temperature of rare to medium-rare depending on preference. The exact technique for cooking is up to you. I tend to do a two level fire for searing and then finishing, but the exact method depends on the type of grill, thickness of the cut, etc. If you would like some smoke flavor, you can throw some wood chips on while cooking like this and see what you get. The short time and frequency with which you tend the meat / open the grill may make this completely ineffective, but it's worth trying to see if you get some smoke flavor, if that's what you really want.
Best Answer
1) Chicken is a tough meat to cook right, in that it dries out very easily. A few too many minutes of cooking and you can go from a deliciously juicy piece of chicken to a dry and chalky piece of chicken.
If you're newer to cooking chicken, I highly recommend using a meat thermometer and taking the meat off the heat about 5-10 degrees before the final temperature is reached, as the meat will continue to rise in internal temperature during the resting period.
For cuts of chicken, it doesn't really matter. I personally like chicken breast, which is white meat and is lower in fat. But chicken thighs (dark meat) are also great, and tend to be juicier by default because of a higher fat content. The entire chicken is great!
Start with some known chicken recipes, which include cooking times and spice/marinade combinations. Once you try a few, you'll get an idea of how to experiment on your own.
Chicken Breast Recipes
2) It will depend how you intend to cook and eat the meat. If you just want a piece of beef, you're going to usually want what's traditionally considered a steak. This will be a NY Strip, Rib Eye, Tenderloin (Filet Mignon), Porterhouse, and many more. Stay away from Chuck (stew beef), Round, Flank, Sirloin etc. These cuts are tougher and require more than just grilling or baking to become enjoyable (although can be very enjoyable when marinated, or slow cooked).
Well done meat isn't always tough - I highly suspect it was the cut of meat you were trying to prepare in your other question. Although, most people will find well done meat less enjoyable than, say, medium-rare or similar. This is preference though - so eat what you find most enjoyable. (although if you have not tried a medium-rare NY Strip or Porterhouse, I recommend it!)
3) This entirely depends on how you cook the meat and what cut of meat you start with. Things like Chuck are usually cheaper than NY Strip, because they are tougher to start with, and contain more connective tissue that must be broken down before it can be enjoyed. For example, Sirloin is usually a bit tougher than a NY Strip, however if marinaded and slow cooked properly, it can be turned into a delicate, tender and delicious Tri-Tip! Same goes for Flank, which when marinated properly can be turned into delicious carne asada for "street tacos".
For more tips on how to prepare and cook your meat, see your other question: What am I doing wrong when cooking meat?
If you have the ability to find it, I highly recommend watching some episodes of Alton Brown's Good Eats tv show. It's fantastic, and doesn't just explain how to cook something - it explains the why reasoning behind cooking things a certain way. This will equip you with the knowledge necessary to experiment on your own without a recipe!