Under JAR, you need a license before starting a type rating.
Not true. There is no restriction on the type or class of aircraft that can be used for PPL training. The problem is in meeting all of the requirements for issue of the licence and class/type rating if anything other than an SEP is used.
And turbo-props require a type rating
Not always. There are SET class ratings as well.
Training in a "high performance aircraft" (there is no such category in JAR....
Not true. A number of aircraft are categorised by the JAA as 'HPA', requiring extra training at ATPL level in addition to the relevant class or type rating course. [I-2021 beat me to this bit]
Whilst this is all very welll in theory, the bottom line, as has already been stated, is that it is
usually not practical and/or financially viable to learn on anything more complicated than an SEP. If, however, you wished to buy a high performance aircraft, and you could find a suitably qualified instructor and approved training organisation (it couldn't be done in a Registered Facility) prepared to take you on, there is nothing to prevent you doing so. Whether it would be a wise thing to do is quite another matter.