chatter: ski shovel edges grab the snow and let it go very fast, multiple times per second. It feels like the fronts of the skis are making tiny flapping movements up and down. It's jarring, like when you are driving a car over a rippled dirt road. I don't think this is what Vickieski is describing.
wobble: I think Vickieski said the fronts of the skis go back and forth. I'm thinking this means sideways, left and right. This can be caused by several issues:
1. Boots could be too big and loose on your feet. If your feet can shift leftie-rightie inside the boots even a little bit, then you have no control over those skis and they will do what they want. Check the boot fit first. Use boots whose labelled size is two sizes smaller than your street shoes, if you are renting. Too-large boots are very common. If you buy boots, be sure to get them at a reputable ski shop and get them very snug; they will become more comfortable with a few days of skiing on them and they will help you have control over those skis. Getting boots fitted properly by a reputable bootfitter at a real ski shop is more important than the type of skis you buy.
2. You could easily be skiing from the backseat. If you stand on the skis such that most of your weight is over the back part of the skis, it's like driving a car with the front two wheels in the air. When you are going slow, or when you have the skis flat on the snow, you have no control over the shovels of your skis if there is no weight up front pressuring them down onto the snow. I've seen lots of skiers with air visible under the shovels. They can't see it, though, and have no idea this is the case. Those unweighted ski tips will move left and right as they please. Skiiing from the back seat is very common too. If this is the case, take a lesson so a ski pro can watch you ski and help you get your stance fixed. Doing this will open up all kinds of possibilities for your skiing, and help you feel more in control all over the mountain.
3. This third option is an odd one, but I've had it happen to me. If the bottoms of the skis have become convex, like the hull of a kayak, then they will certainly shift left and right. I think this happened to mine once because someone tuned them in a shop incorrectly. If this is the case, have your skis stone-ground and that should solve the problem. If you've had the wobbling happen with different rental skis, then this is not the problem.
4. Ski length and ski flex should not be causing this problem. Ski on any length and type of ski you like. Seek the solution to this problem in the boot fit and/or the way you ski.
Best of luck, and have fun this season!