So at a first glance, if you were in controller.com or trade-a-plane; what are your first initial criteria’s (Say on a Piper Arrow II or III with a budget of no more than $80k)?
You know, I do it so much I had to actually look at Controller to see what I do.
First thing is to get to the page with the type I'm looking for, and sort by price (ascending). IMO, the people who don't put an asking price on their plane are more likely to just be fishing. If there's an example that meets all my other criteria and I'm ready to buy I might consider it, but generally with the more common models there are others that do have prices listed, and they're going to get my call first. That also helps to weed out the "But honey, the airplane's for sale, nobody's buying it!" pricing. If you see a poorly equipped, high time airplane in the middle of a bunch of newer, nicer airplanes, chances are they're not particularly interested in selling it. So, I start looking from the cheap end.
If you're looking for particular years and such due to particular features, put those in the search... But honestly, I usually don't do that anyway because I've seen enough aircraft that were improperly listed in various ways. You might be able to score a good deal on a 310R that is listed as a 1974 model, for example, if all the other 310R shoppers listed model years 75-81 because that's when they were produced. Once in a while you might find a "1997" instead of "1979" and the people looking at the specific model years are going to miss that. So, get used to being able to spot the physical characteristics of the plane you want. Better example in your case: Look at the Arrow IV listings to see if any of them have straight tails.
Next: Skip over the ones that aren't in the US. With a rarer bird, maybe one that's not in the US but is still N registered, but again that's a rare case. Importing airplanes is very expensive (ensuring type compliance, maintenance compliance, ferrying or shipping, etc) so generally not worth it.
Then, I open a new browser tab for each airplane, and go through them at a high level first. Look at the AFTT and engine times, glance at the pictures, eliminate any that have glaring issues. Often a look at the panel will tell you that this plane is going to need a lot of work to get to what you want it to be, and usually they're not priced low enough for it to be worthwhile for you to do that work, so you can often eliminate a few at the low end of the price scale there too.
Then, I look at them in a little more detail. For each one: Does it have an autopilot? (And you'll need to make sure all modes of the autopilot work, especially on the factory-original Piper Autocontrol ones.) Bonus points if it's got a newer 2-axis autopilot, at least an S-TEC 30 or equivalent (unless you're already budgeting/planning for a G5/GFC 500 install). Does it have a color IFR GPS? Garmin GNS or GTN series, Avidyne IFD series, etc. Does it have an engine monitor? Does it have any avionics that are unserviceable if they break? What's the condition of the paint and interior, and will those need to be done soon?
Finally, I take the remaining contenders and put them into a spreadsheet I created that allows me to easily compare the asking price to both Vref and to a "me value" that also adds in the must-have and highly-desired options (and the cost of installing them if not present) to the equation. The airplanes that are priced the best relative to the "me value" are the first ones that get contacted... And sometimes, I only contact one!
1) A Turbo might be cheaper, because people are scared of them.
... or don't need them in the first place.
2) A Turbo might have better avionics, because most people flying them are doing IFR XC missions. This is especially true of autopilots, where you are more likely to get something better than the old Piper Auto Control III (which is a good autopilot for something that is beyond ancient, as long as you keep it on HDG or vector it right onto an ILS and use LOC mode) that you see in the NA Arrows.
True.
3) It is correct that your typical mission suggests you don't need a Turbo. That said, are you ever going over the Appalachians? Landing at airports in them in the summer? Might help then.
The highest point in the Appalachians is 6,684 feet, which can be cleared by a safe margin easily in a normally aspirated airplane. Very few airports actually up in them, either.
5) A Turbo will be faster.
No, it won't, until you get up into the teens. And it takes time to get up and down as well. So, if you fly a lot of shorter legs, the turbo will end up slowing you down. Long legs where you climb into the mid to high teens are where a turbo aircraft will shine, but you really need to be flying 300+ nm legs on a regular basis to make it worthwhile. At 5000 feet a turbo gets you nothing worthwhile.
A Garmin 430W or better in good working order and less than 1000 hours on the engine.
IMO, there's nothing wrong with higher time engines, if the airplane is priced appropriately.
There are certainly a variety of opinions, from "doesn't matter" to "lower time is always better" to what I posted above. I've had the advantage of being on a flying club BoD, intimately involved with keeping the airplanes maintained and paid for, with other people's money and with a few other people to bounce ideas off of and discuss strategies. And, I did that long enough that I was also involved in turning over our entire fleet, so I've been able to buy airplanes with other people's money too. 
I don't think so.
