I haven't hand loaded since 1999 because the federal government said they'd put me in prison again if I did. They also told me they put me there in 1999 because of my knowledge and my business. I can keep my hands of the guns OK but they will never stop me from spreading the information I want to spread, short of prison or death.
I said all that to say two things. 1. I'm not current on the powders that are available today nor how they compare to what was prior to 1999, and that doesn't matter anyhow, as the primary thrust of your question as I see it is how to deal with shortages in our rapidly changing times. 2. The information I'm going to give you below is the type which big brother hates like the plague. And I'm going to give you a bushel basket full.
Cast bullets work well with any powder suited to the cartridge and jacketed bullets. Watch the burning rate if you want to wring out maximum power, but if full throttle isn't high on your agenda one doesn't need a lot of different powders.
When purchasing powders, as a general rule, buy ball powder if one is available in the approximate burning rate you need. They burn cooler than either flake or extruded powders, which make them far easier on throats. I don't know about all ball powders, but for 296 and H110, which are the same powder, the pressure curve is a straight line up to 100,000 psi, whereas all the stick and older flake powders take off into la la land when pressure hits 40,000 psi. In my experience, using ball powders with burning rates similar to 4198 -3031 etc, the ball powders could be loaded to far higher pressure/velocity than the stick powders before leading starts, so I'm going to presume. To clear your thinking on what I'm saying about pressure climb. Pressure is considered a straight climb when one adds a given amount of powder and gets a relatively uniform increase in pressure/velocity for each increment. Since 50,000 to 60,000 psi is safe pressure in most bottle neck rifle cartridges, if a powder is used that gives a pressure spike when loads are increased beyond about 40,000 psi, developing loads can be difficult with tiny powder increases often causing the barrel to start leading. Say we chronograph our loads and get 100 fps with each grain of powder increase but when pressure reaches the powders pressure spike point, 40,000 above, adding a grain gives a 150 fps velocity gain. We are pushing into the pressure limit of that powder.
You wanted me to name three or four powders that would work well with all the guns you named, so I'll name a few which are great if they are available, but don't get choked up if you can't get them tomorrow. If you can get a selection of powders you can keep loading, once I show you how to mix things around a little.
1. Hodgen Universal is the cleanest burning powder I've ever used for light to moderate handgun loads and its a super ignighter powder if you can get powders that are too slow to give good performance. I'm speaking primarily here of the bottle neck rifle cartridges you named. Universal will make real nice plinky loads in all the guns you named, burning with excellent uniformity with charges as low as 3 grains in a 30-06. (Some powders will hardly burn with such light loads.)
2. H110, 296 will wring your magnum handguns out for maximum power, but also make excellent rifle powder, and have been the most popular Schutzen competition powder for years. (Low velocity plainbase bullet rifle loads.) Because of the straight pressure climb these will allow much higher velocity in rifles than 2400 and will give 4198 a close run if not beat it when max power is wanted from a light charge of powder. You could live quite well with only these two powders.
3. Any of the ball powders suited to 223 class cartridges will beat 3031 for power and give excellent results with cast. H335 is one of the slowest listed for 223 I believe, and is very well suited for a broad range of velocities in your rifle cartridges.
4. 748 is a favorite of mine for 308/30-06 class cartridges with cast, as I don't load either to their limit with lead. These four powders will give you a realy good selection for about any kind of load, though a slower burning powder than 748 will wring more out of the 30-06.
WC-820, a surplus powder which was made for the M1 carbine is a super powder with about 10% faster burning rate than 296 but similar burning characteristics. Accurate #9 was originally WC820 but when stocks ran out they had new lots manufactured. I've never tried the new stuff, but expect it would be close to to old powder at least, and very serviceable for the same uses. I have burned as little as 4 gr of WC820 in 30-06 and it gave excellent velocity uniformity. (Going that light was just a test for low velocity cast suitability.) If you find any available from surplus powder sellers, get it, but look hard at any offering you see if the burning rate fits into the range of powders listed for jacketed in the loading manuals. You'll find burning rate charts in most modern loading manuals.
Mixing powders.- I once accidentally dumped a powder measure full of Blue dot powder into maybe 3 or 4 pounds of 2400. I shook it up well then poured out some from the top, the middle and the bottom, and loaded a few rounds with each. Chronograph speed was the same for all, and slightly faster than with straight 2400, which meant slightly higher pressure. I used it all up. I have mixed powder several times since with similar excellent results. In each case though I mixed only ball powders with burning rates not too far apart. My goal was to use up small lots of powder accumulated from military ammo which I broke down, and the results were excellent.
If you have access to lots of black powder but don't want all the soot and 30 foot jet of smoke, mixing it with a fast burning flake powder has worked very well for me. One can get far higher velocity than with either straight black or just the fast pistol powder, when loading for rifle cartridges. Or put about any relatively fast smokeless powder down on the primer and cap it off with enough black powder to get good compression. Quite frankly I'm going into survival wisdom here. It's more practical loading all smokeless powder if it is available.
If you can lay hands on very slow burning cannon powder or powder from dismantled 50 BMG ammo, you might find the velocities to anemic in your 30-06. A bit of flake powder for an ignighter down on the primer and the coarse powder compressed over it will get things moving a lot better. Just adjust the ignighter charge up a little at a time, backing off on the slow powder as needed so you can compress it when you seat the bullet, working gradually up till you get good snappy ignition and a clean burn, or even raise velocity up to that of the most well suited powders. I've forgotten what the cannon powder I had was, but compressed loads only gave 1900-2000 fps with heavy cast in my 30-06. By loading 2400 or 296 under it in sufficient quantity I was able to get velocities similar to 4831, which is probably the best max velocity 30-06 powder I've ever used. Survival loading again. Tuck this information under you belt in case you ever need it. But don't mess with it just to save money if proper powder is available, even at high cost.
Probably most have heard of using granulated plastic shot buffer over the powder for cast bullet rifle loads. Cream of wheat was popular before shot buffer came out. Hardwood sawdust is also excellent. Again, get the shot buffer if you can, and every cast bullet loading bench should have some if rifle cartridges will be loaded. It does wonders for shot to shot uniformity, and will wipe leading from the bore with loads that are far too hot if filler isn't used. If you are working up a load and begin to get leading before you reach the velocity desired, back the charge down a bit before adding filler, as the resultant compressed charge causes higher pressure. If you can't get gas checks, any of these fillers will help you wring maximum possible velocity from bullets without gas checks. The check shank doesn't matter, and don't try to lube it. Just fill the grooves, and work up your load. I have obtained 2000 fps with plainbase lead bullets in 30-06 by using fillered loads, with excellent and very usable hunting accuracy, though not up to what I could get with gas checks.
I hope this answered your questions thoroughly, and puts a lot of reloaders a bit more at ease.