On the sickness thing, it's also interesting that a fair number of people comment on feeling sick travelling on Pendolinos.
As for the trains built, there was the APT-E, which was Gas Turbine powered and largely successful, but was never intended to be anything more than experimental. It's main downside was that Gas Turbines were costly to build, maintain and run, so a similar production design would have struggled to be economic, wheras at that time diesel engines couldn't produce the power to weight ratio needed.
The APT-P was the electric version, and was a prototype for a series of production trains to be built for the WCML. One big problem was that it was rushed into production before all of the lessons from APT-E could be learned, and then it was rushed into service before it's own problems were sorted. Futher mistakes were having the press run in the middle of winter in cold and snowy conditions (something that can cause trouble for all transport), which lead to problems with the hydrokinetic brake fluid freezing, and as has been said, to serve lots of alcohol which almost certainly increased the reports of motion sickness. The desire for a top speed in excess of 140mph required 2 powercars, which for various reasons had to be in the centre of the train, which therefore was made of 2 identical half sets, yet speeds above 125mph were never achieved due to lack of cab signalling. 3 trains were built in total, and only one survives.
The planned production train was the APT-S for Squadron. These were to be similar to the APT, with tilting, articulated vehicles, but with a lower top speed of 140mph, which allowed just 1 powercar at one end of the train, with a driving trailer at the other end. Having the powercar at one end of the train also allowed it to not tilt (since the seated driver could experiance higher cornering forces than potentially standing or walking passengers or crew), and this allowed the elimination of equipment to keep the pantograph level on the wires. Due to the problems with the APT-P, these were cancelled before production began.
A further simplified design was the APT-U (can't remember what that stands for). This was to be similar to the APT-S, but without articulation, and using passive rarther than active tilt. This allowed it to be much cheaper and simpler. This was also cancelled, but a modified version was supplied to the Eastern Region for use on the newly electrified ECML. The main alteration from the APT-U was that rarther than being a unit, it became a loco and coaching stock push pull set, with the loco able to work trains independantly. To distance it from the APT, the trains were originally called "Electra" and later "Intercity 225", with the locos designated Class 91 and the coaching stock Mk4.
The knowledge of tilting trains gained from the APT was passed on to other countries who also wished to experiment, in particular Italy, who developed the passive or Pendular tilt into the Pendolino, so whilst the APT might have been a "failure" it's decendants live on on both the WCML and the ECML.