This problem has different solutions depending on how you want to play.
If you're just looking for the achievement, one solution to your problem is to do whatever missions you want, choosing the side of good, until you get relatively close to your level point. Then go into a town and steal (for minor karmic reduction) or lay waste to entire towns (for major karmic reduction). You can quickly lower your karma this way. Then, once you're neutral, go kill some random creatures until you level.
(If you're looking to steal, a good place to do it is at Dukov's place… he's got stuff everywhere.)
The "nice" thing about this system is that if you stay on the path of "good" the whole time, you can do this at each achievement point: be bad until you get to the right karmic level, level up, get your achievement, and then restore a save to get back to your good self. You can quickly get "good", "neutral", and "evil" achievements for all levels on one playthrough this way.
(I did this, because I don't really enjoy long-term playing as an evil character… but I do like my achievements!)
You could also do this as an evil or neutral character, but it's much easier to quickly drop from "good" down to your new goal, than to work your way up.
If you find that you're close to leveling, and you're at the right karmic level, and don't want to take a chance on changing your Karma by doing a story-type adventure, you can always go wandering looking for random bad people to take out. Going near the Washington Mall can get you some XP fairly quickly, and you can go inside the capitol building and clear out large areas without picking up any Karma, positive or negative.
Unfortunately, I'm not sure your goal is achievable, as there are generic citizens in some of the major cities -- "Megaton Settlers" and "Rivet City Guards" for instance, that while you may wipe out all of them for once, they will eventually respawn.
The other issue is that you are unable to kill children (with good reason!) so the children within Megaton, Rivet City, Little Lamplight, and assorted other locations will still be around.
As to actual ramifications, the biggest would be repair. Some of the best armor / weapons in the game (or at least, the most unique) are either hard to come by replacement parts, or flat out impossible (in the case of T51-b Power Armor, Chinese Stealth Armor, etc). You'd want to make sure you either only use equipment that you can repair on your own, or face the grim reality of your coolest toys breaking.
Though after you've killed every killable NPC, what exactly do you have left to kill anyway, hm? :P
Best Answer
If you're just starting out, I suggest following the main quest until you reach a city (like Megaton) and then explore that city for side quests.
Generally, the game will take you to places that you can handle, and then give you quests you can handle while you're there. If you do all/most of the sidequests, you'll level up enough to be ready for the next plot mission.
Once you have a few levels under your belt, you'll be better able to handle yourself against the random encounters of the wasteland, and you can do a bit more exploring.
While traveling in the wasteland, save before you leave a safe location, and then save often (ideally in a different slot than your "safe" save). This is overly paranoid - the game's not THAT unforgiving, but if you want to avoid the frustration of dying constantly, it helps.
That said, here are some general tips for the early game:
Weapon-wise, it depends on what your character has points in. Pistols are easy to find and the ammo is plentiful in the early game. Rifles can do more damage and at a longer range. Energy weapons and big guns I usually leave for the mid to late game, but they can do a lot of damage against targets that would normally shrug off small arms fire.