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Welcome to the H&R forum here at TFL
There is a lot of good info available from the guys here. Second the suggestion to get a couple of good manuals, also recommend a book like The ABC's of Reloading, and if you have a decent reloading section in a sporting goods store near you the powder companies all put out small free booklets with a slightly limited amount of data. Most of the powder and bullet companies also have data available on their websites.
The Lee kit is a great way to get started in reloading without spending a bunch of money. I have used one for quite a while reloading for 5 rifle calibers and 4 handgun. A good friend, the guy that got me started reloading, has 2 Lee presses bolted on his bench. He loads at least twice as many calibers and probably at least 5 times as much ammo as I do, and his equipment was far from new when I met him 10 years ago.
There is not one powder that would work well/safely in all three of the calibers that you mention. I mostly use Varget in my .223, with 50-55 grain bullets.
good luck,
bergie
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