Well, not quite. I'm sure it can get a bit confusing.
The simple answer is that your Blackhawk can safely shoot any factory .45 Colt factory ammo, is suitable for deer season, and if (and only if) handloaded will exceed the .44 Magnum. Read on for more
Basically, Ruger is known for over-building their guns. The Blackhawk platform is the one most well-known for being strong enough to handle the high-pressure .45 Long Colt loads--it's built almost as strong as a .454 Casull, so people load almost to .454 levels, in .45 cases. Ruger of course does not advise this as this is a liability for them.
High pressure handloads in this cartridge are also called "Ruger Only" loads, so you can safely handload using "Ruger Only" data. Sticking to factory loads won't hurt anything though (any factory load, +P or otherwise, should be safe in a Blackhawk). Regarding hollowpoints, bullet selection will depend on your intended purpose. For something like whitetails, yes; for bear, solid lead would be better.
If you want a bigger bang than .45 LC +P but don't handload, then yes, you'd want to get the .44 Mag.
For whitetail, the .45 LC is an adequate round. Just be sure of what loading you're using and keep its effective range in mind. It would only be advisable to hunt with standard pressure rounds at very close range.
*note* Ruger produces/produced several Blackhawk models, so be sure yours is one of the ones that can handle hot loads if you decide to load to that level