I've got to agree with Chuck on this one. There seems to be a perceived need in general avaiation to categorize aircraft for no good reason I can see. "Complex"? What's complex about it, a few extra controls and instruments, which as previously stated, are only used a few times per flight anyway? I actually find that some of the older, more basic aircraft are more "complex" to fly than their newer versions. The complexity only becomes noticable when things are going wrong. Other than that, it's just a few extra checklist items. A J3, with no accelerator pump, can get pretty comlex at the worst possible time, if you jam the throttle!
Indeed, "complex" aircraft are often easier to fly, because some systems are more automated. What's more complex trying to start a piston or a turbine? In going from a Schweizer 300 to a Hughes 500D during training, I found the 500 much less complex from an engine managment standpoint. Push the button, turn on the fuel at the right time, and watch. The 300 is much more complex to start, particuarly if you're trying to not exceed limitations!
A DHC Turbo Beaver is similarly much more trouble free to start than it's pistion brother, which is more complex? After recently applying to be added to a Cessna 172 insurance policy, the agent called and asked me: "How many of your 3000 hours in single engine Cessnas are actually on 172's?". As my pilot report lists single Cessnas from 140 through 210 without missing many, I informed the agent that it really did not matter how many were on a 172. Eventually they agreed, and that was that.
Simply answered (lest I be accused of not answering the original question), Fly anything and everything you can get you hands on, as early in your learning as you can. Don't yet the school try and talk you out of it. When I was learning to fly, the school's C177RG was the top of the heap. With 80 hours total time, they insisted on a 5 hour checkout for me. No problem, 3 of it was a night cross counrty under the hood. That was good use of my rental dollar! (by the way, at the time, that plane rented for $55 per hour wet, those were the days!) I put more than 100 hours on that beauty before someone wrecked it. That was all that was needed to be insured on most singles, and I have not had a problem (other than the aforementioned insurance agent) since!
Pilot DAR