Confabulous
When you talk about complex aircraft which are ex-military on the civil register, the JP is not complex. Complex is the most complex of all categories, and requires manufacturer support to get on the register. The next category down is intermediate.......
In terms of piston aircraft, you may be thinking "complex" in terms of retractable undercarriage and wobbly prop. Simpler than an Archer in terms of engine handling and management ? Not in my opinion - but Nigel can probably give you a better view on that. Some issues to think about on an axial flow compressor are the time taken to spool up on short finals (engine management here being very important), and what to do if you get a compressor stall. (You'll feel the banging under your feet as the JPT starts rising.) You'll also need to think about hot starts, possible bird ingestion into the intakes, the different rates of fuel consumption with different RPMs set at different altitudes - for example the Viper can be twice as efficient in terms of lbs fuel burnt per knt travelled at 30,000 ft, than it is at sea level.
But all this is very manageable for the average PPL so long as he is properly trained / converted to type. A word of caution to you though - some of the insurance companies specify minimum hours before you'll get cover. I think 100 -125 hrs is the minimum for JPs. If you look at the delta web site, you'll see 300hrs P1 is their requirement to fly the Gnat.
I hope to see or hear of you flying these aircraft at some point in the future!