Important Starting Steps:
GETTING TO VEGAS:
First things first. Head up to Vegas. I take the direct route north. Avoiding the Deathclaws is possible if you skirt past Black Mountain, keep to stealth and hug the mountains north of Black Mountain so you're not on flat ground until you've curved around East a little bit.
The general route is north to Yangtze Memorial, then head east northeast to Sloan. There may be a Giant Radscorpion spawned if you go too far north but if you go more east than north to the railroad tracks you can avoid him.
From Sloan head east northeast to Neil's Shack. From there it's northeast until you spot a gap in the rocks that is full of bear traps, and a rolling boulder trap. Trigger the rolling boulder trap and retreat to let it go past, then disable the bear traps and head up.
From there you want to stay on the rocks where even if a Deathclaw sees you they can't path up to you and head mostly east. If you head a good ways east you can sprint north to the Grab 'n Gulp without much opposition. If you don't go East enough you can run into the fiends near Allied Technologies Office, you might be able to take them but with your limited firepower they may be tough. If you feel up to it it's a good way to get a gun upgrade if you can snag a laser or a shotgun.
From sharecropper farms you can get up to Gun Runners without any enemies, and then to the Freeside gate.
This route does some important things. Gun Runners is an important vendor because they carry plenty of guns and ammo and usually enough caps to make selling a snap. Plus they are about 10 steps from the fast-travel spawn point, making those repeated selling trips easier. NCR Sharecropper Farms has a skill book (see next section) and is a good central hub for your explorations.
If you want a companion you can dip south in relative safety to pick up Veronica.
Free skill points are a very good thing.
Now some books you won't be able to get to until you're higher level. Because they're hidden behind a swarm of Cazadores (Brewer's Beer Bootlegging), a level-75 lock (Repconn HQ) or require higher-end quests to get to (Followers Safehouse, the Suite at The Tops). But there are tons of skillbooks you CAN get to quickly and easily. Or if not quickly or all that easily at least can get to without certain death.
After heading north, go on south and stop by the Lonewolf Radio, Primm's Bison Steve and the Police HQ and Nipton Road Rest Stop. Keep an eye out for Star Bottlecaps as you go, you'll be going a lot of places you don't necessarily want to have to slog back to.
Keeping to roads usually avoids the biggest of the big nasties (Cazadore swarms and Deathclaws) but keep a few things in mind. The middle and south of the map are generally fairly safe from the worst nasties. Go too far south (below searchlight) and you run the risk of a Ghoul Reaver encounter, however. the mountains to the west have Cazadores, save the run to Red Rock Canyon north from Goodsprings for when you have a good fast-RoF gun and decent health.
You can take a little shortcut to Bitter Springs and the skill books in that area by starting at Camp Golf or thereabouts, swimming to the middle of lake Mead and going north. There will be Cazadores at the boat ramp to Bitter Springs Recreational Area. But Cazadores are two things if they're anything: way too aggressive and poor swimmers. You can get their attention and dive underwater and they'll follow you right in, unable to sting underwater, and drown themselves.
Another goal of your skill book spree is to unlock fast travel locations in most areas of the map so you won't have to trek over miles of wilderness to get to any quest you get. I hit up Jacobstown, Novac, I88, Boulder City, Bitter Springs and the highlights of the New Vegas area that I can safely get to while I get my skill books, star caps and while you're at it get the snowglobes too.
This is actually the most difficult part of the game. Once you're up to level 6 or 7 and sitting on hundreds of bonus skill points things get a LOT easier.
FARMING FOR FUN AND PROFITS:
Once I get a good chunk of skill books and need to boost my combat abilities to get to the rest, it's time to start building my power base.
Now I usually do the quests as far as Nipton at this point, for a change of pace and because I have to go into some of those areas to get skill books ANYWAY.
No matter what your actual weapon specialization is, you're going to have to use guns for a while. Actually until you have a reliable source of tons and tons of microfusion and small energy cells, stick to guns or melee. Farming fiends works but I always carry a small gun or two for use on little enemies that would be a waste of an expensive microfusion cell. Powder Gangers drop massive amounts of 9mm ammo and 9mm guns, even the occasional 10mm or shotgun.
A shotgun is an amazing weapon even up to level 10 or so with even an energy weapon user for use on weaker enemies without much DT.
Melee has it far easier, and can just farm for what gives the best cap rewards, usually fiends with their more expensive energy weapons.
Fiends have the advantage of giving Karma as well. If you're going for a low-karma playthrough avoid fiends all you can. And because of this never be an energy specialist as a low-karma character.