Buy a couple reloading manuals (Lyman 49th and Hornady are good) and read them a couple times. This will also help you shop for powder for the calibers you listed. There are tons of powder you could use for those calibers but you'll find that some powders are next to impossible to find both in shops and online.
Free online data from Hodgdon here:
http://www.hodgdonreloading.com/
I'm going to list powders that are readily available. You should be able to find them at shops like Cabelas, Glenn's Ammo in N. Reading, Al's in Derry, Shooters Outpost, and Rileys etc. No sense in me recommending powders like Bullseye when you won't find it very easily.
Anyway, for 9mm, 45, and 38 spl, you can't wrong with HP-38/Win 231 (same powders), Titegroup, CFE pistol to name a few
For 357 mag, I would recommend H110/Win 296 (same powders) if you're looking to load true magnum loads, not mousefart loads.
I'm new to 223/556 and have only loaded 55 gr FMJs with H335 (meters well) but there are lots of other powders you could use. No experience loading .308 but I do load 30-06 and 7.5x55 swiss with IMR-4064 powder (meters really bad unless using a Lee perfect powder measure). With rifle it really depends on your use. I only shoot out to 120 yards so 55 gr FMJs for .223 and 168 gr bullets for 30-06 are plenty good for that distance. If you're looking for benchrest accuracy out to 300-600 yards you'll probably want heavier bullets which I have no experience with - I'll let the veteran rifle reloaders chime in for that.
And yes get a tumber for cleaning your brass. This is the one I've been using for 3+ years. Works great and comes with everything you need - all for $102 shipped
https://www.berrysmfg.com/item/media-separator-kit
You'll also need things like a scale, caliper, bullet puller etc.
Reloading pistol is a breeze but rifle is a whole different animal with A LOT more steps involved. You'll need case lube, case trimmers, and a chamfering/deburring tool for rifle. If you're doing high volume rifle shooting, there are tools like the Giraud tri way trimmer that work well at trimming/chamfering/deburring all in one - just need a cordless drill.
http://www.giraudtool.com/Tri Way Trimmer.htm