If you have enough time, maybe the best way to visit the complex is by bicycle. Long dirty roads along big lakes, visiting the most remote ruins of the city is a great experience. There are some places in Anuradhapura new city to rent them.
The best way to get around Anuradhapura really is by bike. If you're not up to that then you can negotiate with a three-wheeler to drive you around, but bargain hard for a decent price. The sites are too spread out to make walking an option. Bicycles are available for rent at most guesthouses for around Rs 250 per day.