What do you consider to be a high base stat total...?

Patience, young grasshopper....

Statistically speaking, your average fully-evolved Pokemon gets a BST in the 400-500 range, depending on when/how it evolves. Starters (and a few outliers) have a BST in the 540 or so range, while pseudolegendaries top the chart at 600 (with actual legendaries starting at about 560 or so). Slaking is definitely an outlier at 670 (tied with a few version mascots), but at the price of being Truant.

For me personally, I'd say it depends on how I use the individual Pokemon, but it's usually the 500 level.
 
I don't count stats that I don't see as helpful for a Pokémon, like Attack for some 'mons that specialize in Special Attacks and vice versa. So factoring that, it's around 500 that I consider to be high.
 
For standard fully evolved Pokemon that isn't a legendary or pseudo legendary, I consider the average stat total to be about 480. From there, I'd consider Pokemon with a stat total of 500 or over to be "above average". It'd be interesting to see where the uppermost quartile of the stats for these Pokemon begins, that's what I'd consider to be the benchmark for a "high" BST.
 
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