How long will it take a new pilot to start flying more advanced planes like a Cirrus SR22T or Piper Malibu?
You have a few questions here that should be addressed individually. 


  What is a realistic path for me?


Get your PPL then start to consider what you can fly/own. As you train you will inevitably learn about the various major airframes people fly and what it takes to own one. 

As a word to the wise you should read this thread about a young guy who figured he could get his PPL and buy the fastest plane out there for his mission. Its lengthy but paints a good picture of reality. 

If you are flying long distances alone and don't need the useful load, like speed, and want to stay in your budget you should take a look at the Mooney's. You can get one of a few models they have made since the 90's for well within your budget. 

You should join AOPA and make use of their resources to get more information on owning and buying a plane. They have been a great resource in my recent plane search. They can give you a realistic idea on finance options as well as what your insurance rates are going to look like. 

As for whats common (at least what I have seen) to some extent depends on your flight school and the quality of the planes. Many people do their VFR PPL in a rented plane (C172 or PA-28 being the most common). Then those that really like it and are serious about it look to buy an entry level plane to do the IFR in as well as build hours, get to know the national airspace system and just fly fly fly. Many buy what they trained in or step up a bit to something like an M20C or Arrow etc. Once they have their IFR the trips get bigger, longer and you really start to cross some distance. At this point you can expect anywhere from a few hundred hours to upwards of well more than that depending on how much spare time you have to fly around. Generally speaking most owners I have spoken to put about 100 hours on their plane every year (unless they use it actively for business).  

To flat out answer the question, we must first say "it depends" but generally speaking I would say it will take you in the ball park of 300-500 hours to get into a high performance complex plane like a TTx or SR22 at least from what I have seen. Although to be honest some people train in an SR22 (see the above linked thread discussion, that guy trained in an SR22). The Malibu is a bit of a different beast and would take more time to get into. You can realistically fly 500 hours in 2 years if you fly ALOT, at a regular pace expect it to take 4 to 5 years to get to that point. 

Legally, you can go buy an SR22 right now, pay a hefty insurance premium and do all your training in it. As long as you complete what ever the insurance company wants you to do, you can fly the plane. The broader question is "should you?..."


  At what point is it reasonable for me to safely and legally pilot
  these high performance planes?


The reality of this will come down largely to your insurance company and what they will allow you to fly for an affordable insurance premium. You list quite a range of planes here but generally if you want to fly high performance/complex airplanes your insurance company will look favorably if not mandate an instrument rating. For a turbine and or cabin class aircraft a commercial ticket wont hurt but is not necessary by any means. There will be some checkout hours required for any of these planes before you can fly them solo but the general expectation is that you are stepping up into them from another personal plane, or from a lot of hours in a rented plane. Most high performance newer aircraft will also sport a glass cockpit setup (G1000 or Avidyne etc). Insurance companies (and just common safety sense) will want to see some glass time if you plan on stepping into a plane like this. 

Legally speaking you will need at least a PPL as well as a high performance endorsement (as all of these planes are over 200HP) and a complex endorsement for the Malibu as it has folding gear, moveable flaps and a variable pitch propellor. For a pressurized plane you will also need a high altitude check out. 


  How would you suggest I get from newbie to mission capable?


The same way every pilot does, fly and fly often. There are no short cuts in aviation training. Nothing can replace time in the left seat. Plenty of people go from nothing to flying for the airlines in just a few years. However in that time they log a lot of hours (over 1500 to be exact) and they train in all kinds of scenarios. 

The most important thing to keep in mind is to be patient, your PPL training will be hampered by weather, broken planes, busy instructors, delayed check rides and all sorts of things. This happens to everyone and you should not let it paint a negative picture for you or discourage you.