In general terms, the butt is the 'heavy mono' that transitions the diameter and energy of the fly line into the leader, through the mid section referred to as the taper, then into the tippet.
The size of the butt depends on what's on either end... the fly line style and the tippet/fly. Generally, the bigger the fly line, the higher the grains and energy coming down the shock wave. Diameter is also a concern, they say if you step down too radically in diameter is affects the loop's energy transfer. Makes sense.
Lines come with a 1 foot straight extension on the fly end past the front taper. Many cut this off or shorten it for sinking lines to reduce the belly when sinking a fly. For int/floating lines if it doesn't bother you, just leave it I guess. If you did chop the tag end you could add a foot of leader to the usual length for additional stealth(?)
Anyway, the point is you want the forward end of the line to be graduating down in diameter and grains to roll the loop over at the end of the cast. Too radical of a step downward and the energy won't transfer well, and not enough will not provide a graceful landing for the fly.
Specific fisheries have different criteria. Saltwater coastal guys are not very concerned with finesse, more with heavy flies and strength for big fish. I've been known to fish a three part leader - 40# butt, 30# taper, 20# tippet (if you can call it that) for very short sinking head leaders when I need to get a big fly deep quickly. If I split the taper into two parts I end up with a 15# tippet but the most common leader I tie is the 5 part tapering down to 15# (40/30/25/20/15) at 60%/20%/20% ratios.
When Spey casting the leader design plays a big part, you want the leader to act like a true extension of the 'contrived roll cast' that Spey casting is. You get used to anchoring the fly a certain way and the wrong leader configuration can really mess you up sometimes. I usually tie a 6 part leader for Spey casting, 2 part 60/40% butt, 3 part taper, and tippet. Essentially a very long trout taper in bigger diameters. I usually start with a 30# butt section and taper down to 8# or 10#.
Trout require a lot of finesse as you know and leaders are a critical part of dry fly presentations. I usually just buy trout leaders but have tied my own. One nice thing is to know exactly what I need to replace if anything goes wrong when I tie them myself. With knotless I never know how much to replace, etc. The butt diameters are significantly lower than the above two to match the lighter lines and transition to the tippet over the length of the leader.
I am sure someone who knows more about leaders than I will help you more. I am a meat and potatoes kind of leader tyer... A.J. McClane's 60/20/20 rule.