I concur with all the other comments. You've got plenty of brass for all these cartridges handy to do a ton of load development, so I'd just pick one and go for it. Keep in mind that you may have to try 2-3 different powders before you find a load your gun likes, which also means you may need a few hundred bullets and primers at the same time. You might get lucky on the first try, but who really wants to stop there? :wink: Just a word to the wise though, store your powder cans away from your bench, and only have 1 type of powder on the bench (or in your powder thrower) at a time. Keeps you (and them) from getting mixed up.
You can hand clean all your brass just fine with a can of Nevr-Dull (Walmart, Auto Zone, O'Reilly's) - it's a roll of cotton soaked in metal polish. Just pull off a chunk, polish your brass by hand and wipe it off with a clean cloth. It'll even make new brass even shinier! It doesn't do anything for the buildup of powder residue inside the cases, but I figure the cases will wear out before you get enough buildup to really matter. Some people think tumbling is necessary, but for hunting accuracy I don't think it does. Still, if you come to Conway very often feel free to drop your brass off and I'll tumble it for you :thumb:
Those Handi Rifles typically have a long throat, so if you're gonna load for them, stick with the prescribed OAL in your manuals. You've probably been told that accuracy is best if you seat just a few thousandths off the lands, but that only works if you can keep enough of the bullet in the neck of the brass to hold it. Generally you want to seat the bullet into the neck no less than the width of the bullet (i.e. for your .243 you want at least .243" of the bullet seated into the neck of your brass). With a long throat you can't do that, especially on light-for-caliber bullets. Seating bullets really long also spikes the pressure, and will actually decrease your accuracy potential if the throat is long enough (like on my NEF .270). Anyway, I'd stick with the normal OAL for now and try seating to the lands after you've had a bit more experience.