Despite what many may say, I'll say go big in your gun choice. Sure people have taken them with .30-30s, even .357s. But how much of that was a lucky shot in the exact killing spot.
Some bears drop instantly, but a lot of those will get up and run. They don't bleed a lot with many handgun rounds.
Many PA bears are very big. Some are very tough to bring down.
I've been fortunate enough to take 8 black bears and 2 brown bears. Only 3 did not move- one brownie with a .375 JDJ Contender at 30 yds. coming at me with a shot just under the chin; one black with a .375/.284 XP-100 and a 260 gr. Nosler AB on a double shoulder shot at 160 yds. ; one brownie with a .500 Mag. and 375 gr. X at 129 yds with a double shoulder shot.
Others shot with .44s, .325 WSM, and one with a double lung shot with the .375/.284 and 260 AB ran a bunch ,but were recovered. Blood trails were spoty. All were decent hits.
For that reason my bear gun this year is my .416 Taylor Encore with Horn. 400 gr. DGX. Laugh?? I hate chasing bears. I'm getting too old for that.
For your .44 I'd go with 250 Keiths. For your .35, Nos. PTs or Xs.
Bears are wonderers. Very hard to pattern unless they have natural "baits", i.e. corn, apples, cherries.
Good luck.