Most of my understanding of philosophy is from a historical perspective; which is why I focused so much on how it's actually practiced (or rather, not practiced; beyond surface-level interpretations) by the majority. I would appreciate, however, any recommendations people might have for more in-depth research into particular philosophies.
For the Stoics I’ll quote what I said to
@Hlaalu Agent:
Meditations by Marcus Aurelius and On the Shortness of Life by Seneca are a good introduction to Stoicism.
Discourses and Selected writings by Epictetus is also a good book but is a little more preachy than either of the above.
Letters from a Stoic by, again, Seneca is also decent from what I remember of it.
For Discourses and Letters I’d recommend the Penguin translations, while I’d recommend the Gregory Hays translation for Meditations.
These are the main four I can think of off the top of my head, though it’s been years since I’ve read any of them. I lost my paperback copies, and haven’t picked up an electronic one yet. I have been meaning to by a new copy of Meditations, as it was the best of the lot from what I remember of them.
On the flip side is one of the other most influential philosophy of the Roman period, Epicureanism.
In Epicureanism, the pursuit of pleasure and avoidance of pain are of paramount importance and both are necessary for a happy life. In that way, Epicureanism is a hedonistic philosophy but it differs from other such philosophy in that it advocates for a simple life.
“Accustom yourself to the belief that death is of no concern to us, since all good and evil lie in sensation and sensation ends with death. Therefore the true belief that death is nothing to us makes a mortal life happy, not by adding to it an infinite time, but by taking away the desire for immortality. For there is no reason why the man who is thoroughly assured that there is nothing to fear in death should find anything to fear in life. So, too, he is foolish who says that he fears death, not because it will be painful when it comes, but because the anticipation of it is painful; for that which is no burden when it is present gives pain to no purpose when it is anticipated. Death, the most dreaded of evils, is therefore of no concern to us; for while we exist death is not present, and when death is present we no longer exist. It is therefore nothing either to the living or to the dead since it is not present to the living, and the dead no longer are.” -Epicurus,
Letter to Menoeceus
“It is better for you to be free of fear lying upon a pallet, than to have a golden couch and a rich table and be full of trouble.” -Epicurus.
Epicureanism is ultimately an atheistic materialist philosophy rooted in what mankind understands of the natural laws of the universe. It concerns itself less with the acquisition of wealth or other physical pleasures and more with the pleasures of the mind and the abandonment of fear or worry.
An epicurean is thus less concerned with acquiring physical objects than with making good friends and living a joyful life as free as he can make himself. What matters to an epicurean is that you aren’t hungry, thirsty, or cold. What you are eating, drinking, or taking shelter in matters less than how much comfort you take in it.
On the Nature of the Universe by
Lucretius would be a good start.
I personally find the dynamic between Epicureanism and Stoicism fascinating. 
