If you're looking for the BEST way to get to and from the Disneyland Resort specifically, look no further than the Disneyland Resort Express
I have always used this service when travelling to the Disneyland Resort area without a rental car and have always been pleased with it. The service is usually great and is probably the best value as far as shuttles go! The Disneyland Resort Express is owned and operated by Southern California Grayline... so you can expect a big, comfy, spacious tour bus to be picking you up. It even has the current Disneyland promotions as decals on the side of the bus so it really makes it feel like official Disney transportation, even though they are only affiliated with Disney. And if you book through All Anaheim Tours (the link I provided you with above), you will find it at the cheapest price of any other website that offers it as well. Don't worry about it being sketchy, I've used this website many times and it is prefectly professional and legit. You could also try scheduling a SuperShuttle, but my first pick is and will always be the Disneyland Resort Express! I wish you a happy first visit, be sure to get your "1st Visit" buttons at City Hall on Main Street USA!