Obviously there are ways to increase your income, but I'm considering that outside the scope of this answer, and focusing on getting better prices.
Discounts
Some vendors will give you discounts for actions taken in the game, like Carla giving you a discount for making a sarcastic remark when you meet her. Shopping at vendors that give you a discount will help.
Raising Charisma
Much like raising intelligence for additional xp, you can raise your charisma for better prices. I keep a set of charisma gear on me, including clothes (+1-3 CHA), a hat (+1 CHA), and glasses (+1 CHA). I put these on before speaking with vendors, and it improves both buying and selling prices.
As an experiment, my character with 3 CHA sold some items without the CHA equipment (3 CHA), then I loaded and sold the same items with the equipment (7 CHA). I got approximately 200 caps without, and approximately 250 caps with.
You could also drink some alcohol first, which should pay for itself.
Perks
There's a perk for better buying and selling prices, called Cap Collector. I haven't tried this, but the exact numbers are listed on the fallout wikia.
You can also improve buying and selling prices with the perks you receive from finding Tales of Junktown Jerky Vendor magazines.
Other Items
Some specific items will give you a boost specifically to prices. Grape Mentats will give you 10% better prices and +5 Charisma for 8 minutes.
Your ability to sneak is affected by 8 different factors:
- Equipment weight: Although you said there was no difference, there is a difference if you walk. The heavier the armor or weapon, the further you'll be heard if you move. However, if you stand still, your armor weight won't affect you at all.
- Light sources: Light sources also influence your ability to sneak heavily. However, this only affects you if an enemy has a clear LoS on you. If you are in a lit room with no enemy being able to see inside, the light does not affect you at all.
- Your agility skill: The more agility you have, the more difficult you become to spot when sneaking. This affects you in both moving and not moving.
- Perception of the enemy: This is also a huge factor which both affects you moving or not moving.
- Distance: Obviously, the further the enemy is away, the hard it will be for him to spot you.
- Any form of contact: If you touch an enemy, he will immediately spot you.
- Loud Weapons: Any form of attacking an enemy will make them spot you. However, silenced pistols, melee weapons and grenades/mines will not break your stealth, although it will cause the caution alert if you do not kill them in one hit. Grenades always cause caution alert if there are any alive enemies in the area.
- Special gear: There are several modifications like shadowed which can improve your ability to sneak. Also, gear obtained from legendary enemies can have a stealth-improving effect on you.
Your pip-boy (includes the torchlight) do not affect stealth at all as you already found out. You can also listen to radio while sneaking and nobody will notice.
Best Answer
I'm more than a day into a playthrough with a stealth ninja melee character. I get these animations fairly often.
I'm primarily using General Chao's Revenge and Blitz to melee guys from far away, sometimes behind, sometimes not. Sometimes I sort of chop their heads off, sometimes I impale them through the chest, sometimes I jab the sword straight downward through the top of their ribcage near the collarbone. That last animation takes forever.
I can confirm that they happen in VATS when stealth attacking humans.
I believe I've also got such an animation at least once out of VATS, but I am using VATS almost exclusively. I recall getting these animations regardless of the angle at which I'm facing the enemy, but note that VATS places me behind them when it executes the attack. I don't recall ever getting such an animation on a non-humanoid enemy.
I find these animations annoying, and wish I could turn them off. They delay being able to act again for a while after leaving VATS, which has gotten me killed more than once when there was another person around I didn't see before attacking.
Assuming that you've met the criteria for a backstab animation to be possible, the animation actually occurring seems random. Sometimes it happens, sometimes it doesn't.
It's possible the animations may only trigger with certain weapons. Try a combat knife or a Chinese officer's sword. I've gotten them with both of those for sure.