Bullseye is the best powder of the 3 you have. 3.5gr of bullseye pushing a 158gr lead bullet has been a standard load for decades that has proven to be extremely accurate.
Lead bullets are faster than jacketed
coated bullets are faster than lead
A couple of 38spl loads for a 686 competitor.
When I load 38spl's for a 357, I like to load the bullets long. The h&g #50 148gr button nosed wc is crimped in the middle lube groove (been doing that since the 80's). And the 640 158gr rfn hp is crimped in the bottom (has 2 crimp grooves) crimp groove.
Coated bullets are also allot cleaner with allot less fouling allowing the user to maintain accuracy longer and keep cleaner hands/less junk when handling the speedloader and cylinder. What the 686 looks like after a typical 200 round range session with the 640/bullseye load.
148gr hbwc's can be used but you have to watch the load/pressure. Too hot and the skirts blow off and stick in the bbl. 2.7gr/2.8gr loads of bullseye have been used for years with hbwc's. Depends on the firearm but typical velocities are around 775fps with that combo. I like to use american select with hbwc's, a little more velocity 800fps+ with less pressure (around 13,500psi). I've cast my own hbwc's and swaged my own hbwc's for decades. This allows me to make them out of harder alloys. Harder alloys ='s more pressure/faster loads.
Another excellent 38spl load is that 3.5gr load of international clays and a 158gr bullet. Pictured above/far right target. It's cleaner burning than bullseye and gets a little more velocity for the same bullet/load combo.
While titegroup is a good powder, it doesn't play well with lead bullets. And it loves coated bullets as much as it loves powder hoppers.