I've actually made four dresses from the books and I'm here to tell you that unless you are a) really willing to experiment, b) willing to mess up, and c) have a lot of time, those are really tough dresses to make and to make them look right. If you've got all that, though, I say carry on!
What fabric you use depends on the dress. If you want to make the ones that more appear in the manga, honestly I'd say go for a nice, quality cotton. Oftentimes, too, what I find really makes a costume is the details. For instance, if Chi is wearing a plain white dress, get one of the white cottons that has a very subtle design in it, like the kind used for quilting. Those can really vamp a costume from cheesy to authentic.
For something dressier, like something with more ruffle than dress, lol, you'll want to go with something more satin, like Jasdero said, or at least something with shine. Remember, Chobits is based on the gothic lolita style, so stick within those color bounds, but also make sure your dress is made with quality satins. Many you can get are flimsy and seethrough and are actually much more difficult to sew with than the kind you have to pay a bit more for, but it's really worth it. I used a cheaper sateen on the corset I made but a nicer one for the skirt and the skirt was so much easier to work with.
There's always a couple rules of thumb with sewing. If something stands out, like a poofy skirt, use a stiffer fabric. If it clings, go thin. Easy stuff, and if you ask for help in a fabric store there will be someone happy to direct you.
Most of all, it really depends on how formal the dress is. Remember that you can do ruffles with lace, and feel free to experiment a bit! These are fun, cute dresses. Be prepared to spend a few hours hand-sewing lace, but it will pay off in the end.
Good luck with your costume! Hope I haven't scared you off too much
