You've got a lot of posters talking about specific planes, but you're asking about the process. I think specific planes comes next. Here would be more of a process related thought. If I were in your shoes, here's what I would try to think through:
1) Identify exactly what it is that you actually want to do with this plane - the classic "what's your mission" question. Define this first, but also be open to feedback about your mission (as in, if you said your mission was to fly to Aspen with 6 people and bags in winter storms on a regular basis, you're going to get feedback like "that's not realistic for where you're at as a pilot"). Defining your mission includes numerous criteria:
- How much weight are you likely hauling? Of what type (people [how big are they], gear, baggage, etc)
- How far do you typically want to go?
- What are the places like that you want to go? Paved runways, grass, dirt, off-airport?
- Where are you located and what kind of terrain do you envision flying over?
- What is your tolerance for time in the airplane?
2) Understand your financial capability. What's a reasonable purchasing budget and how much are you committed or willing to spend on operating and maintaining the aircraft per year? A strong recommendation is to slightly undershoot your financial capability, it will be a lot more enjoyable that way. But, don't cheap out either.
3) Once you have those two figured out, post it here. Some may give you a lot of flack for posting a subject that has been hashed out 100 times before, but secretly, they all love it. You'll get plenty of responses and ideas. Hash out your own ideas in that thread.
4) Ideally, go take a look at a couple of the examples that surface in step #3. The idea of attending a big airshow is a good one, but in my experience, it's pretty hard to "test drive" planes - I bought my first plane without ever having flown that model and I didn't even get to test fly it before purchase - sometimes that's just how it goes.
As a side comment, I would buy a plane whenever you're ready. No reason, IMO, to wait until after PPL and definitely no reason not to train in it for IR. I bought my plane after PPL and did all my IR training in it and it was great. There are plenty of additional recommendations and debates along the way (high time vs. low time, fully equipped or plans-to-update, insurance costs and coverage availability, buy now or buy later, buy the plane you will want in the future now vs. buy the plane you're actually experienced for today) but those all come down the line.
PS - It will be hard to get this perfect. Eventually you'll buy a second plane anyway. Just try to get it "good enough" so that it lasts you 5-6 years.