I really liked Fallout 3 and so on a whim (and understanding that Fallout 3 plays nothing like its predecessors) I decided to pick up the Fallout Trilogy Pack. The problem is I'm not very familiar with the style of gameplay in those games. I'm not sure exactly how to accomplish some of the quests I encounter. Some of the initial tasks send me toward areas where there are enemies that are way out of my league or require me to somehow obtain a ridiculous amount of money. For instance, in order for me to skin Geckos (I'm hoping the skins will help me obtain better items in barters) I need to save the trader. However, he is in a cave filled with strong enemies. I find myself barely surviving one encounter before I have to exit the area and run back to my village to get healed (I've already consumed all of my healing items).
 
Am I doing something fundamentally wrong? Is there a certain order in which I should tackle tasks or some alternative solutions that I'm missing? Some helpful tips would be much appreciated.

Start with low level quests and work your way up. 

Start small. Even if you're getting hard quests from the get-go, don't take on anything you can't handle. If you head somewhere and see that the enemies are too much, turn around and go do something else until you're well levelled and well equipped. Quests that don't need combat are the best ones to level up with, but that would depend on how you've allocated your skill points. Talking you way out of stuff early in the game is a good way to rack up experience.
 
Beyond that, kill every small thing you find and try your best to slowly get your level higher. Sooner or later you'll be beating the toughest enemies in the game like they were nothing. Just gotta keep at it.
 
Edit- I should clarify that what I mean by quests that involve no combat are the best, I mean that they're the best for early on, as you can level up and allocate skill points to your combat skills as well.

Most of my RPG experience comes from playing console JRPG's, so my initial reaction was to start grinding through random battles to get stronger. Suffice it to say that I quickly found out that wasn't a very effective way to play this game...

" Most of my RPG experience comes from playing console JRPG's, so my initial reaction was to start grinding through random battles to get stronger. Suffice it to say that I quickly found out that wasn't a very effective way to play this game... "

Fallout 2 is much harder, on the whole, than the original game or Fallout 3. You need to be persistent for the first third of the game, basically. Save often, and all that. 
 
It won't take terribly long to become an absolute killing machine, though.

slowly. dont scare it