We always take a cab. It costs about $40, and they have van cabs at the ready, so even if you have a big group, you can get to your hotel cheaply and directly.
I wouldn't think so for a cab. I know for the shuttles, you just walk outside to the shuttle area and they will put you on the first one heading to the Disneyland hotels.
It depends on how many people in your party. Super Shuttle is $10 per person each way. There's a coupon in the Entertainment book for $2 off per person when you book online. So my daughter and I are getting round trip for $32, plus a tip. $8 per person each way, can't really beat it. However if the whole family were going, 5 of us, that would be $40 each way, even with the discount. For 4 or more people, might as well take a taxi; it is your own private vehicle (Super Shuttle may have to make other stops) and there's a $40 flat fee.
You can take the Disney Resort Express bus, too, which is kind of nice and fairly convenient, though a bit more expensive. I believe it's $25 per person RT, $17 for kids. It stops at the 3 DL hotels first, then the other hotels. It's operated by Grayline: http://graylineanaheim.com/docs/GL Anaheim DRE Brochure 2008.pdf
Hope that helps!
Edit: cabs don't provide car seats. You don't legally have to have one if you take the Grayline DL Express Bus, though.
If you really really don't want to take the carseat, just go with the Disneyland Express bus. Can't have a carseat on a bus seat, since there are no seatbelts!