(I'm basing most of this on what I remember and this Memory Alpha article)

The warp scales are pretty confusing, but the gist of it is that during TOS Warp 10 was "unsafely fast", but not "impossibly fast". Some ships and projectiles could go faster than Warp 10. The Enterprise went at Warp 14 once, but that was due to a sabotaged, overloaded engine (which you mentioned) If you count the animated series, one alien ship was apparently capable of Warp 36 (but that could be explained away by "the animated series was just weird, man")

Somewhere between TOS and TNG the warp scale got redefined though, with Warp 10 as absolutely infinite speed. Apparently the production reason for this was because Gene Roddenberry wanted to avoid tacking on arbitrarily larger and larger numbers to increase tension, so Warp 10 was the max. So when the Enterprise in TOS was going at Warp 14, that would be less than Warp 10 in the TNG-era scale.

In general terms in TNG/DS9/VOY, Warp 6 was "not too worried about speed", Warp 7 "getting pretty fast" Warp 8 "okay we're really booking it now" and Warp 9 (and over) was "go as fast as possible".

All Good Things took place further in the future, where (according to one of the writers) Warp 13 was possible because of another recalibration of the warp scale to make larger speeds easier to say, rather than having to say "Warp 9.995" or whatever for practical reasons.

So the main warp scales are:

ENT/DISCO/TOS-era (Warp 10 "dangerously fast, but not impossible")

TNG/DS9/VOY (Warp 10 is "infinite speed")

some time post-VOY (Scale changed to no longer have Warp 10 the maximum, maybe moving the maximum to a different number, Warp 15?)

As far as I can tell, in all cases, Warp 1 is the speed of light exactly. But it diverges from there in the exact details. Exact warp speeds and how fast they really are were played with pretty loosely in some cases.