One major difference between design philosophy of Fallout 1 versus Fallout 3 is that in the Interplay games, you're not necessarily meant to be able to tackle every obstacle the game throws at you.
As an example, in Fallout 3 you might wander into tougher zones than were intended for your level but otherwise if you go into a dungeon you're expected to be able to get through it one way or another. Fallout 1 sort of gives you a series of obstacles and it's up to you to figure out if it's worth trying to get through it or if you should hold off until later.
It has been a couple of years since I played the game, so I'm going to be lacking in specifics. I'm not sure if Vault 15 was intended to be one of the very first places you go to, so that might be part of it. (You should at least be going to Shady Sands and working up some experience in there before heading out on your own too much.)
Especially in terms of combat - running away is actually considered a viable tactic in the old Fallout games. (Especially the random encounters - you're just not going to be able to tackle a lot of them early on. You do kind of hit a point where you're going to essentially be a walking tank of destruction though.)
The other thing to keep in mind is the sort of character you've made. If you haven't built a character for combat, then you need to be looking for other ways towards an objective. All character builds are (generally) equally "workable" but it's usually a matter of playing to your strengths. If you're putting more points into Speech than Small Guns, for instance - then yeah, combat's going to be tough and you have to lean on your companions more than your combat skills.
Anyway, even as a fan of turn-based games I have to admit that Fallout (at least in terms of combat mechanics) was no Jagged Alliance or X-Com. (Honestly, the mechanics didn't really hit their stride until Fallout Tactics, to my mind.) At the time, I thought the graphics were pretty good, though some parts have aged better than others.
The series' big selling point at the time was the degree of freedom (and most importantly meaningful freedom.) You can do whatever you want and almost every obstacle put before you has more than one approach to it. Many of the choices have later ramifications, and often not what you'd expect. Remember, this was before every RPG had a good/evil meter tacked on to it. This was a game that realistically tracked your actions and those choices impacted the world and the NPCs views of you, without really feeling a need to enforce a morality on it.