I can tell you this about dry yeast. I only do fairly heavy ales, and ferment indoors in the house with no chilling, and I have used US-05, BE-134, BE-256, and Voss Kveik. Maybe one or two others. NEVER had any problems with those except that the Voss is a real monster at summer temps with a big beer. With dry, I have always just sprinkled right on the wort. Easy Sneezy. These days, I harvest, and make a starter, which is actually no work at all. I just brew an extra quart or two of wort, and take out for the starter for the batch, then 5 gallons go into filling up the no-chill cube which will no-chill chill for 24 hours. The starter gets the ice water bath chill, then the harvested yeast from the last batch gets pitched into it. By the time the wort is ready for the fermenter, the starter is going bananas, on the exact same wort that I will be pitching it to. And if it ever fails to take off in 24 hours I can still pull a pack of dry yeast out of the fridge, where I almost always have a sachet of at least one of the above named dry yeasts. But the starter made with the previous batch yeast harvest always gets going way way quicker than pitching dry yeast.
The only liquid I have ever used is HotHead, and that only because it is or was only available as liquid.
Keep your dry yeast cool and it will keep for a long time. All you have to do with most of them is sprinkle, though you can of course make a starter the day before, if you want a faster takeoff.
I have also poured new wort right into the recently vacated fermenter with the yeast cake still in it from the last batch. Other than making the new yeast cake twice as thick and usually completely covering the spigot, no apparent issues with that, but I don't let the yeast cake sit and sit for weeks, either. I try to give the old cake some new wort by the next day or the day after.
Old hops and grain trash and stuff settle out first, before yeast, so when transferring new wort in, don't stir or overly disturb the cake beyond the top layer. You don't have to mix it up. The little yeasties will soon be muching, getting fat, reproducing, and floating and swimming up to the top without any deliberate mixing.
You can harvest and wash yeast, or you can just scoop some off the top of the cake and dump it in a zip lock bag and put it in the fridge for up to a month or so. Good idea to sanitize your scooper and the container you will put it in. The scoop and dump approach could give you some issues if the next batch is lighter than the batch the yeast came from, or if you dig down and get a lot of nasty old hops trub. The top layer should be pretty clean stuff. I have never bothered washing but I might if I decide to try freezing.