I recently bought a PS4 and Destiny and the physical copy of Destiny (purchased at Walmart) was just the base game. I had to purchase the Taken King on PSN. I would recommend going to the Taken King straightaway. You can do the year one content first. Frankly, there's not a lot of it and it's not that great compared to the newer stuff. With your purchase of The Taken King you'll get an item that will bring 1 character to level 25 (high enough to start TTK content) and a set of level 25 gear.
As far as difficulty, most of the TTK content (story quests and strikes) aren't significantly harder than the old stuff, other than higher level gear. The main "hard" content are the raids, and those will require some learning.
One thing to note is that the item that levels you up does not level your sub-class, so you'll still need to learn your skills at the same rate.