Well come to the forum.
As for being quiet - not with the current generation of 1ZZ-FE engines - these noted to be noisy engines since they changed to an all aluminum engine design design with better efficiency, lighter in weight, smaller packaging, and most noticeably dropped the relatively quiet timing belt in favor of the long lifespan timing chain.
Things that they added between the 2003-2004 and the 2005 Corollas:
- now uses the CAN computer interface instead of ISO (need to have a CAN compliant scanner - most new ones are).
- emissions from ULEV to LEVII-ULEV status
- charcoal prefilters filters added
- ECTS-i introduced
- engine immobilizer
- Tire pressure warning system
- DBW throttle system
Reliability is about the same - if you following that old adage of never to buy the first generation of anything - the 2005 is kind of a awkward spot - as it has many fixes over the previous two models years, but also added a host of new features.
I'd have the car thoughly inspected by a dealership or a very good independant garage that specializes with imports, preferably Toyotas. As for the quietness - Corolla is no Lexus. There will be higher levels of NVH, but usually better than most other cars in its class.