Going back to the original question, the basics of deciding the order are these:
Range from touchdown. Simple and obvious, and certainly the first consideration.
Speed. A C172 with 20 miles to run will end up behind a 737 with 40 miles to run. But... a jet with 40 to run behind a turboprop with 35 to run could still be No2. The jet WILL have to slow down and this is part of the decision-making process. Something like an ATP will usually be screwed regardless in a busy sequence, because 215kts from 50 miles away doesn't fit the flow. A D328 or DHC8-400 will be able to do 250kts+ all the way to base leg, which is more than most jets will manage.
Orderliness. When you have a busy sequence, and certainly if you're No6 or higher you can bet the approach controller is working pretty hard, it's in everyones' interests that the sequence be manageable. This may end up, on occasion, being slightly unfair to someone, but avoids situations getting out of hand. Using the ATP at 215 kts as an example, putting in a downwind and running in a couple of straight-ins ahead of it, or cutting somebody fast infront via a base leg with vertical separation from the ATP, can expedite the overall sequence and make it easier to control. Peeling aircraft off opposing downwinds is easy and you can pretty much keep doing it all day, so when the guy at the back calls MAYDAY you have easier option to get him on the ground quickly (peel him off while everybody else continues downwind, for one).
As an adjunct to that, straight-in approaches are a relative rarity at Edinburgh, usually the guys from Northern Europe coming accross the North Sea for 24. Judging a straight-in against one in the rush from the south is made much harder by the fact that with , say, 30 miles from touchdown, the 2 aircraft are 20 miles or so apart. If there is a busy sequence already when the straight-in arrives on the screen, it's more manageable to give him a dogleg onto base.
And finally.... if there are enough aircraft that you have one infront of you by 6 miles (or maybe 4 miles these days?) on final and one behind you by the same distance, approach is doing a pretty good job and you aren't being punished! There are simply enough aircraft inbound to make runway capacity a limiting factor.