Beeline the main quest, up until chapter 3 or 4. There are a lot of things you can't do or can't buy until certain chapter milestones are met.
Most of the 'locked' weapons are story unlocks.
You can't fence stolen horses or carts until you unlock the relevant fences. Stolen horses can be sold at stables for a small amount, though.
You can donate stolen items to the camp before unlocking the fence, which is a good way to clean your inventory and unlock camp upgrades.
There's a fast travel map that is unlocked once you upgrade Dutch's and Arthur's tents. It's not super exciting, though. You can only use it to go from camp to a location, not from anywhere.
Carriages can be used to fast travel between major settlements. They cost money, and will appear as "unavailable" if you're on your horse. Your horse will follow the carriage, so it will arrive at the destination with you.
While on horseback and holding the "gallop" button, you can enter the cinematic camera by holding the "camera distance change" button. while in the cinematic camera, your horse will auto-follow roads towards a waypoint. However, for whatever reason this mechanic will occasionally ram you headfirst into a tree, another rider, or some other person/object.
Thrown weapons are great for increasing your max health. They hit hard and fast, and give you a lot of health XP per hit/kill. Try to use them up when you get into a big fight and you'll have maxed health in no time.
Sprint around a lot. Most of the time you'll be on horseback going from place to place, but your max stamina won't increase without doing a lot of sprinting.
Core meters drain over time, or they drain quickly if you continue to push your health or stamina after the bars have drained. The health and stamina bars will recharge as long as you have "core" remaining.
The deadeye meter doesn't recharge on its own, even if your "deadeye core" is full. You have to get kills outside of deadeye to recharge it.
You will auto-unequip your "long" weapons when riding on your main horse. Whenever you get off, there's a good chance you'll have to re-equip them. The exceptions to the above are if you were actively holding something (like the binoculars or a gun) or if you're not on your main horse.
Getting enough pelts to craft anything interesting takes a lot of effort. The benefits may not be worth it if you don't want to spend hours hunting.
Every animal has a max pelt quality, on a scale of 1 to 3 stars. In order to get a perfect pelt, you have to get a one-hit kill using the right weapon on a 3-star animal.
Binoculars can help you determine the quality of the animal pelt and they can also show info about what the optimal weapon is.
As mentioned in the linked article, legendary animals don't have pelt quality. Go nuts with your most powerful weapons and shoot them wherever.
If you've got a fast horse and a lot of patience, you can lasso animals and knife them to preserve pelts
Get a varmint rifle early, it's the best weapon for a lot of smaller animals, and it's one of the weapons you won't get for free from the story missions.
If you die, anything stored in 'horse cargo' is lost. If you find a perfect pelt you need for crafting, make a beeline for your camp!
If you die, your horse will show up when you wake up, but if your horse dies and you either abandon it or you die before reviving it, the horse is dead and gone forever.
Most of the best horses must be bought, but at least in the early game, it's much better to catch your own. Catching early game horses is quite easy, and often yields horses that would normally cost $50+.
Certain bits of horse gear actually modify stats. The saddle, stirrups, and saddle bags make a difference. The other items are just cosmetic.
Mild Spoilers Below
The end of chapter 4 brings significant changes to the game. Past this point, you won't be able to donate to the camp or upgrade it again. Most of the camp services will be gone as well.
Sidequests I hadn't finished by the end of the main story (chapter 6) were still available post-epilogue (2 additional chapters). I don't know if all of them carry over, but at least some do.
Any money you have at the end of chapter 6 is gone, but any items or weapons you've purchased carry over to the epilogue.
In the epilogue, you can purchase all the satchels without having to hunt for pelts.