Currently, my character is very much a stealthy sneaky type. Sneak attack critical damage is my favorite thing. This means a very heavy focus on Small Guns, Sneak, and Repair along with perks like Gunslinger and Commando. At level 9, I have:

40 Explosives - Useful for getting out of Minetown in one piece during Moira's quest. You can do it at lower skill levels, but it's a lot easier to disarm Frag Mines when you can stroll up to them rather then having to dash. (Higher skill level in Explosives gives you more time to disarm.) I had a rather nasty time on the Roosevelt Memorial Bridge early on, as it is heavily mined with a dozen or two Frag Mines.

52 Lockpick - I've been slacking on this lately, but 50+ is good enough for the moment.

50 Medicine - There are quests that require at least 40 points in Medicine.

55 Repair - The repair skill is wonderful. Not only can you keep your weapons in high condition, but you can combine two sub-par pieces of loot (such as raider outfits) into a single higher-quality piece that weighs less and will sell for more. I've gone back to carrying around my +5 Repair outfit as the 1 lb of weight is easily recouped in the field when I combine loot down into fewer, higher quality, items.

50 Science - This was at 45 for a long time, but now I'll be able to stop carrying around my +5 Science outfit for a while. And there are some useful benefits to having a higher science skill.

60 Small Guns - That's not counting the +5 skill boost I get from my current outfit. I'll probably dump another 10-15 points into this at level 10, because it's getting rougher out there in the wastelands.

50 Sneak - I wish I had more points to spend here. I'll likely dump 5-10 points here at level 10.

Lagging Skills

Big Guns is still at a measly 15, so I toss any large weapons into my weapons locker in Megaton for use down the road. Same thing for Energy Weapons. The only way that I've been raising those skills is when I find skill books or if I boost an attribute. I'll want to get these higher somewhere down the road, but only if I run into an absolute wall with the sneaky method.

Barter is one that I wish I had bumped up sooner. I've been trickling points into this off and one, but it's still only 25. For the moment, however, it's "good enough" and I always have enough caps (money) to buy all of the useful ammo that I find at vendors and to get my one-of-a-kind weapons repaired. So far I always have about 800-1200 caps, and that number is slowly going up.

Speech is still at 14. Eventually, I'm sure I'll find books that boost this skill.

Basic Loadout

Right now, whenever I leave Megaton, I'm generally carrying 50-55 lbs of gear. With the default STR of 5, that leaves me with 145-150 lbs of carrying capacity for loot that I find while out and about.

Ammo has zero weight, as do all meds, so I always carry the maximum possible. Special loot that has zero weight like pre-war money never gets sold. I keep adding to my stash. Eventually, I'll either sell it in a pinch, or find someone who is willing to trade me something for it.

I do not leave town carrying any food that heals less then 20 points per lb of weight. Better to carry a bunch of Stimpaks, which have zero weight and heal for a heck of a lot more per use. And you can almost always find useable beds around where you can grab an hour or three of shuteye to heal back up.

My rule for loot is generally that it needs to have a value of 8+ caps per lb of weight. Early on, I'll pickup loot with lower ratios. Then, as I get close to my weight capacity, I'll either combine loot using the repair ability or drop stuff that has a low caps/weight ratio.

The only guideline I can give you for "how many X do I need" for chems/meds is that "you'll never have enough". With zero weight, I recommend never selling them, and you'll want to periodically spend some caps to stock up. If you pick your fights carefully, you'll slowly increase the number of meds/chems in your inventory. That way, when things get really crazy, you'll have a large stash to use in a fight.

Attire Loadout (17-22 lb)

Right now, I travel extremely light. I only carry the following gear as standard:

+5 Repair Outfit (1 lb): I have an outfit that I looted back in Vault 101 that is lightweight and boosts my repair skill. Very useful in the early levels for combining items looted into fewer, higher quality items to reduce carrying weight.

+1 Perception Hat (1 lb): There's a few versions of this hat around, but I gladly trade off the 3 DR from most lightweight headgear in exchange for a higher Perception attribute.

Amored Vault 101 Jumpsuit with +5 Small Guns and +5 Energy Weapons (15 lb): This is an early quest reward from Moira if she likes you. It has a decent amount of DR (Damage Reduction) and is lightweight. I have yet to find something better. The major downside is that you're at the mercy of vendors to get it repaired. Raider armor is a close runner-up (15 lbs, similar DR, but no bonus) once you get high enough not to care about the bonuses and want a different look. Eventually, I'll replace this with one of the 20 lb Combat Armor options.

Glasses (0 or 1 lb): There's a variety of eyeglass or other eyewear that I like the look of.

Power armor is 25-40 lbs (net weight), plus another 4 or 5 lbs for the helmet. For a stealthy player, heavier armor makes it a lot harder to sneak around. I'll probably roll a heavy armor character down the road, but this character is very much focused on light armor. I may even go as far as to start wearing really lightweight outfits with almost no DR in exchange for better sneak performance.

Sometimes I'll carry along other +5 skill-boosting pieces (+Science, +Medicine, +Speech) for special use.

Weapon Loadout (38 lb)

(Listed in approximate order of damage done.)

Silenced 10mm Pistol (3 lb): Great for dealing with raiders, or small critters in close quarters (such as radroaches). Not as useful outdoors due to the accuracy, but the zero-noise factor allows you to stay hidden and take multiple shots at an enemy. Has a decent critical damage bonus, so works well for VATS sneak shots to the head.

Hunting Rifle (.32 ammo, 6 lb): This is an excellent medium/long range weapon for use against weaker opponents. At long range, you can often get away with single shots in VATS, then hiding until they stop searching. It also packs a decent enough punch that it's the default weapon I carry while wandering the wastelands.

10mm SMG (5 lb): This replaces the old 10mm pistol that I used to carry. For times when I want the accuracy of a pistol, I use my Silenced 10mm Pistol. Treat this as a 1H assault rifle equivalent that uses 10mm ammo instead of 5.56mm. I generally use this once I start running low on 5.56mm. Or if I'm going up against weaker enemies like raiders at short/medium range.

Combat Shotgun (7 lb): Looks like a single barrel shotgun with a large round ammo container. This is a nasty weapon for close-up work. Wait until a raider gets close, then use VATS to pull off a head shot and watch the raider drop dead. Seems to work well against Mirelurks when they get too close for comfort.

Chinese Assault Rifle (5.56mm, 7 lb): This is a sweet weapon for tunnel clearing or other medium range work against harder opponents. When going up against the nasty stuff, I'll start with a Sniper Rifle, switch to this for medium range, then fall back on the Combat Shotgun in a pinch. Accuracy is not its strong point at long range, but it's extremely deadly at short/medium range.

Sniper Rifle (.308, 10 lb): This is a heavy beast with hard to find ammo, but with great accuracy and hits like a truck if it crits. It's a waste to use it against weaker targets or targets that have been alerted, but it's a very strong opening move against Super Mutants and the like if you can get a sneak attack. In addition, it's a wonderful scope to use when scouting out a distant location.

Basically, I try to carry one Small Gun weapon for each type of Small Gun ammo. And each of them serves a different purpose.

Weapons I Wish I Carried

Dart Gun (3 lbs): Extremely useful against melee/unarmed opponents who have to get close to hurt you. I've been looting the ammo for a while, but have yet to find one or find the schematics.

Scoped .44 Magnum (4 lbs): Not sure why I haven't started carrying this yet, although I keep collecting and buying ammo for it. I should've started carrying it once I took the Gunslinger perk at level 6. It's as accurate as my hunting rifle, does a lot of damage, and very few other weapons use the .44 ammo. I'll probably toss this in the pack on my next outing.

Railway Rifle (9 lbs): This is one of those "really cool" weapons as it shoots railroad spikes. It does lots of damage and is primarily used against enemy limbs (instant crippling effect). It's really only useful at close range due to the projectile speed. I'll probably dig up schematics for this at some point and make one and play around with it. But unless I boost my STR a few more points, there's no room for it in the pack.