A Citation II flight crew; inexperienced in the aircraft; twice slowed below Approach Control's speed assignments while on initial approach and were cleared to make a go around due to multiple aircraft too close in trail. During the go around they suffered two altitude excursions while attempting to utilize the autoflight systems; after which they disconnected the autopilot and flew manually to a successful second approach and landing.

Narrative

While configuring airplane for landing (flaps; gear); airspeed fell below both our 210 KTS and 190 KTS assignments by ATC. Note that both gear-down and landing flaps limitations are 176 KTS for this aircraft.With the field in sight at approximately 1;700 MSL; Approach Control directed us to go around; upon our response of '... field in sight...' ATC replied 'Negative; I've got other aircraft too close behind you ...'Our go around clearance was to climb/maintain 2;000; speed 250 KTS; with vectors. Upon initiating the go around--power-up; new heading; and setting 2;000 in the ALT SEL window--the autopilot was engaged. While accelerating the aircraft climbed rapidly to 2;200 whereupon we reset the auto-flight instruments to correct the error (pitch-down; re-set ALT SEL). The aircraft rapidly over-corrected to approximately 1;800. We then disengaged the autopilot completely and promptly stabilized manually at 2;000 FT. Both deviations were queried by ATC; with pilot not flying response: 'correcting'. The remainder of the go around; second approach and landing were accomplished in normal fashion.This was the first IMC event in high-density airspace for both pilots in this particular aircraft as this is a relatively new owner/operation. After a thorough de-brief regarding this incident we have implemented a testing/training program to reinforce auto-flight system limitations; procedures and performance in similar scenarios. This program includes procedures and VMC practice at higher-than-typical approach speeds to better 'fit in' with high density traffic flows.