Powders for .38 Spl.
First off, welcome to the post. Now I'm going to give you some information that will vary from that already stated. I think your Taurus is a 605, not a 650, as I have one too, and load it extensively for .38 Spl. both for practice, and more serious endeavors. There is one powder that I have used for both applications for many years, and find it superior to most of the newer powders for this caliber. It is SR4756. It is not touchy about load density and can be used in .357 Magnum cases as well.
The old Speer # 8 loading manual has this to say about SR4756 and the .38 Spl. cartridge: "Dupont' SR4756 is listed only as a shotshell powder in the more powerful loadings, but it has proven to be an excellent propellant for heavy loads in handgun cartridges. One of the best for maximum .38 Special loads." The loads I'm going to give you are above SAMMI specification of today, but have never produced any indications of excessive pressure in my Taurus model 605. BTW, the Speer #8 manual listed a maximum load of SR4756 under a 158 gr. SWC cast bullet at 11.0 grains. My loads are no where near that, but I have safely loaded that charge in my S&W model 28. The loads I will give you here are safe in my 605, and I believe will work for your needs, as well.
For low velocity practice loads using Laser Cast 158gr. cast bullets with CCI-500 primers, you can load 4.4 grains of SR4756. I never load this very often, as it is a very light load. Speer #12 says it will clock in at 862fps out of a 6" barrel. I've never fired this load over my Chrony, but know it is very slow albeit accurate out of my 2" 605. This is the starting load in the Speer # 12, and the maximum they show is 4.8 grains.
The +P load is 7.0 grains of SR4756 using the same Laser Cast bullet and CCI primer. This gives an average velocity of 1055 fps out kof my 605. It produces an average deviation of 13, and a standard deviation of 20.7. It groups very well at 15 yards, produces a sharp recoil, but has no extraction problems, and the primers are only slightly flattened. You may chose to work this load up slowly starting with the above lower charge until you get what you are after. I've used this powder for over 30 years, and have see no significant change over the years in its performance. If you're interested, I also have loads using it in .357 cases, as well.