Hi maester steven! Do the nobles or, more likely, the maesters in asoiaf consider the Starks the highest ranking great house, since they’ve been ruling basically forever? Or since andal tradition is stronger in the south, are the arryns preferred? What about the Lannisters? They’re the richest and almost as old as the Arryns. Or are all the great houses equally lesser to the Targaryens and thats all that matters? Sorry for the amount of questions, but also thanks!

I think the heralds’ calculations would be a bit complicated:

• The Starks are the oldest (although the Lannisters might dispute this), but they’re also First Men worshippers of the Old Gods who kept themselves apart from the South by force, so they’re a bit foreign. They’re also relatively poorer than their southron peers, which also counts against them a bit (remember Sansa thinking about Jory Cassel’s fashion during the Hand’s Tourney?). 
• The Lannisters are technically older than the Arryns, but only through the female line (although six thousand years in the male line isn’t anything to sneeze at), so I imagine that’s a point of dispute between those two houses. They’re also the richest, so to the extent that people care about magnificence, that would hold sway. 
• The Arryns are the most Andal of all the Great Houses – they are the rulers of the “promised land” that the Seven showed to the Andals, they even claim descent from Hugor of the Hill himself. So I would imagine that would hold more sway among the pious. (And it doesn’t hurt that they have close ties to the Targaryens as well.)
• The Nymeros-Martells are relatively young, their royal claim only dating back to a thousand years (the Martell half goes back further, but like the Tyrells they didn’t claim kingship). Like the Starks, they are also a bit foreign because of their Rhoynish heritage, and because they held out against the Targaryens – although this is a relatively recent thing and wouldn’t have been an issue prior to 0 BC. 
• Prior to Robert, the Baratheons are a younger house whose claim to royalty comes either from the female line through Argella or through the various Targaryens who’ve married into the family (plus, there’s the whole thing about Orys being a bastard). On the other hand, the Targaryens somewhat reset the rules, discounting longevity in favor of proximity to the Old Blood of Valyria. 
• The Tyrells only have royal blood through the female line, and hold Highgarden due to the favor of Aegon the Conqueror when other houses have a better claim by blood. On the other hand, they rule the largest and most fertile kingdom in Westeros, and they put the most effort into putting on a chivalrous display, so that can’t be discounted. 
• The Tullys have no royal blood, and their kingdom is relatively weak although quite fertile and economically active, so those things balance out to put them somewhere in the middle. 
• The Greyjoys have a pretty ancient claim – the Grey King of the Age of Heroes and the most kingsmoot kings before the Greyirons took over. However, they haven’t been kings for six thousand years, and they rule over a small, poor kingdom of pirates.