Well congrats on getting back in the woods!

Your .270 will be plenty of gun for a bear; it's better to make a good shot with a gun you're not scared of than to risk a bad one with a gun that you're scared of. In your case what matters is not the caliber, but the bullet selection. I don't know what your old man was shooting out of his .303, but if he was using military surplus ammunition, then he was using a bullet that does not expand and therefore was not going to bring good results. You want something that'll mushroom well while penetrating deep. I would personally go with a good soft point bullet like a Federal Powershok (what I use in my .308---they're pretty fast!) or a Remington Core-Lokt (whichever shoots better out of your rifle). If you prefer to use a more expensive bonded bullet like a Hornady Interbond or Nosler Accubond, knock yourself out---whatever your rifle likes. I would be surprised if you don't get an entrance and exit wound out of both. I just simply say not to use a bullet designed for maximum expansion like the Hornady SST; you risk not getting an exit wound in this case, making any tracking difficult.

Also, keep in mind bear anatomy is different than whitetail anatomy, so a good aim point on a whitetail may be terrible placement on a bear. GoogleSearch is your friend in being able to research shot placement from different angles, on different species. There's plenty of pictures online with organs superimposed.

I have no comment on the archery stuff, but someone else will. Good luck!