The business jets are based at CG Air Station Washington. They are used for VIP transportation. The operational fixed wing fleet includes C-130s and H-25s (Falcon). The HU-25 is scheduled to be replaced by HC-144s (CASA CN-235).
Coast Guard aviators are Coast Guard officers first. The Coast Guard officer personnel management system is similar to the other services. The system includes an up or out promotion system and centrally managed assignment process. Typical tours are four years. Assignment to Headquarters in Washington DC, at some point in a 20 year career, is likely. A Coast Guard recruiter would be happy to explain the application process. Coast Guard officers apply for flight training, usually in their first tour after being commissioned. Coast Guard pilots receive their initial training in Navy flight school (same as USMC and USN). C-130 training is done by the USAF, aircraft specific training for the other aircraft is completed at the Coast Guard Aviation Training Center in Mobile AL.
Aviators can request the type of aircraft they will be assigned to and which air station they will be assigned to during initial flight training. Assignments are made according to the needs of the service. Assignment of a first tour aviator to Air Station Washington is unlikely.
The real action in Coast Guard aviation is in helicopters. All aircraft perform a variety of missions. Helicopters do the most interesting missions including armed law enforcement and rescue. There are few experiences that can compare to working together with a highly trained and motivated crew to hoist a survivor from the deck of a sinking vessel in heavy seas at night.
Good luck