"Because, Higgins, some people like woodchuck!"
Exactly! I like their granny smith mix and drink it when I run out of homebrew, which hopefully wont be for at least another six or nine months! In fact I have one bottle left that I purchased before my first batch of this season was finished. It has an SG of 1.014 at room temp. Thats a lot of sugar! I would have guessed less.
You can do better than woodchuck without a lot of effort. If you want a sweet cider and can make do with one or two gallons at a time, the best method IMHO is to get a gallon jug or two of pasteurized fresh squeezed juice with no preservatives from your local produce stand and ferment with ale yeast for 7-9 days, depending on your taste and the apples. Then rack it and stick it in the fridge for a couple of days to chill the yeast out. Rack it one more time into bottles or a pitcher and its good to drink. This way, you are arresting the secondary fermentation which is where the more complex sugars break down and you're not adding anything that might alter the flavor of the apples and yeast, which will still be very fresh. Its like a Beaujolais cider. You can wait a few more weeks to let it clear out if you want, but IMHO there is no need to (and often good reasons NOT to will come along).
You can scale this method up to carboys, but chilling the carboys is a pain. Its a pain that I live with until I find the One True Cider Yeast that leaves enough sugar on its own to achieve the right final sweetness without intervention. I've also had good results mixing a half pound of honey per gallon before fermenting, although then you're getting away from the fresh apple flavor and not as much of a sour note as the woodchuck granny smith, but still pretty damn good. Some say that starting with unpasturized juice and adding camden tastes better. I've personally found this is sometimes true but also less predictable and not worth the extra step. But its your call.
This time of year you should be able to find good to excellent fresh juice at your local produce stand. I would recommend going to several if possible and find the one you like that has the best mix of sweetness and flavor. The yeast will change the flavor somewhat, but it generally cant add flavor. You'll probably need to experiment a little with different yeast to find the best match for the apples. I have had good luck with dry ale yeast and on the recommendations of other posters have just ordered some liquid wheat yeasts to experiment with.
When I am making a cider that I plan to serve to more than a few guests, I make it sweeter than for my own consumption, but not as sweet as woodchuck. More like around 1.006 to 1.010. My friends who brew their own dont like it as much but it gets the booty moving and I keep a couple litres of the good stuff on hand for the hard core ciderheads. You dont need to have as much final sugar in your cider as the woodchuck because the apples will have more flavor if you use good fresh juice and you wont need to mask the flavor of any preservatives.
If you chill for a couple of days and are careful not to pick up any yeast with the final racking, you can bottle it sweet. You might want to let it warm back up to room temp for a couple of days just to make sure the yeast doesnt take off again. I use one liter swing tops although I have never managed to save a bottle longer than a couple of months, so I cant promise how long it will last. If you want something with a little more carbonation, you can chill it for a shorter period, and it will have some fiz, although not nearly as much as woodchuck. For that, you need to make enough to put in a keg and carbonate. You could skip the chilling and just rack it a couple times before putting it in champagne bottles, but IMHO it isnt worth the effort - you need to either be real careful with how much yeast and sugar you leave or be prepared to drink it all on short notice when the tops start blowing off. And make sure you have tops that WILL blow off before the bottles blow up or else it will not have the optimal effect on the S.O.