Especially when first beginning to handload, the MOST CRITICAL step you're going to do in the entire process is get the RIGHT amount of powder into the case. An improperly seated primer will show up when you put the rounds into a box or when you load it into your pistol. A too deep or too proud bullet may change the pressure a bit. But no error or normal deviation is as potentially dangerous, even lethal, as getting too little or too much powder in the case.
So whatever method you use to fill the cases may determine part of your powder choice. No matter what the method, you want to be able to physically SEE into the case after charging with powder. You want to be able to judge "is this the same level of powder I've seen on the other couple hundred rounds I've loaded with this powder load?".
If you use some kind of powder drop device that depends on volume, then you want some kind of powder that flows really well. On the extreme opposite end of the spectrum, if you were to weigh out every single load, then pour that into the case with that little "gold miner's pan" then powder flow is not as much of a factor.
Powders are either BALL, FLAKE, or STICK. That defines the physical shape that the stuff is in. Balls look like tiny balls. Flakes look like tiny corn flakes. Stick looks like tiny pieces of cut spaghetti. Things shaped like balls flow through tubes and funnels and openings better than things shaped like spaghetti. Flake is typically somewhere in the middle.
So for me, I would choose a BALL powder that is well regarded as working well for your intended caliber and bullet style. Read enough online comments in various forums and you'll find more than one usually that fits that bill. HP-38 and W231 will pop up a lot. They are the same powder. Tiny ball shape. Well tested in medium and +P 38 loads. They might be in 357 as well, but I don't load magnums so I simply don't know. That powder is only one example of a proven, popular .38 powder. There are lots of others.
I think it's important to have a powder that has a lot of VOLUME for the weight you're loading. ie, if the load you're running takes up 0.37cc in the case, there's a lot of "dead air" in that case. If some other proven powder took up 0.57cc in the case, there would be less "dead air". That might not make a difference in pressure or accuracy (sometimes it does) but it WILL make a difference in your ability to see the load as being correct. Your human, naked eye can see .57cc better than it can see .37cc when it's down in the bottom of that brass case.
Then load a bunch up. Make up 50 or 100 of your new prospective powder at it's lightest recommended load. Load up another 50 or 100 at each 0.1gr higher till you get to the max recommended load. Then go shoot 'em and take notes. Be subjective, be objective. "This load just feels better". "This load seemed to have tighter groups". "This load kicked harder". Don't shoot all of one load, then move on to the next. Shoot maybe 10 or 20 of one load, then move up, shoot 10 or 20 of the next, move up etc. That way your gun warms up, you get tired, the ambient temp and humidity at your range change, evenly across all the loads.
After all that, pick one you think is great.
Then buy a BUNCH of it.
Then buy a pound or two of something else. Repeat till you die and your wife sells all your reloading stuff on CraigsList for 1/1000th of what you paid for it.
Sgt Lumpy