Personally I liked playing a 10 stat Luck based character. I've only played the game once fairly, but didn't really end it with one of the endings. That's just me; instead I just replayed the game and used a PC mod to grant a perk every level, so I can't speak on much experience for a legit playthrough, especially if you want to use Speech and Charisma. I heard that it's not wise to max any stat because of "Implants," see here: http://fallout.wikia.com/wiki/Fallou...Vegas_implants
For sneaking, get Agi to at least 6 or 7. Silent Running is at 6 AGI. At 24, Slayer req. 7 AGI. At 26 Nerves of Steel req 7 AGI which is particularly useful for VADS players but so late game.
Intelligence boosts skill point gain per level by 0.5 per level, then +10. With an Int stat at 5 you'll get 2.5 + 10 = 12.5 = 12 rounded down. But on your next level up you'll get 13 skill points.
Strength I leave at 5 or 6. The Weapon Handling perk lowers Strength Requirements by 2 so long as you're < 10 strength.
For Perception, leave it at 5 or 6. Better Criticals perk requires 6 in LUCK and PER. If it weren't for this perk I'd leave it low because with ED-E following you get the Enhanced Sensors Perk, which is supposedly equivalent of 10 PER.
I don't think I can make up a good stat build for a proper playthrough, you can probably look at Google for some builds. Just know that balancing out makes you able to use some gear, just not the best. I don't know the best weapons but here's a list of what I found useful. For more info on the gun (probably locations) just look it up on the wiki. The # means the stat requirement. I tend to pick guns over Energy Weapons because I like guns =] but also remember to check your ammo types. I.e. AP rounds are particularly useful for high DT targets (Deathclaws). I ran an Energy Weapon build once just because of the Gauss Rifle which goes pretty far.
Guns: Anti-Material Rifle: #100 STR 8. Lucky: #0, a .357 revolver-> 75 lockpick in Primm (+damage +crit chance). All-American: #100, kinda hard to get but very versatile. Gobi Campaign Scout Rifle: #75 STR 6, Easy to get to req. 100 Lockpick.
Energy: Gauss Rifle YCS/186: #75. Alien Blaster: #75 and Wild Wasteland Trait. Q-35 Matter Modulator: #25, somewhat easy to obtain. AER14 Prototype: #25, EASY to obtain, better than a plain Laser Rifle (no Mods).
Melee: Chance's Knife: #50, fast attack speed and high crit chance modifier for a melee weapon, EASY to get (Goodsprings). Chainsaw: #75 STR 7. Thermic Lance: #100 STR 7
Unarmed: Mantis Gauntlet: #75, high bonus from crits. Ballistic Fist: #100, STR 9. Pushy: #100, Semi-easy to get (deal with Lakelurks), VERY good weapon. Industrial Hand: #75, STR 7. Highest Unarmed DPS weapon, req. Lonesome Road DLC. Zap Glove/Paladin Toaster: #75, useful for Robots/Power Armor.
I don't know anything about Explosives, I don't use them.
Note that # denotes the skill requirement to effectively use the weapon. STR denotes the strength requirement; anything at <=5 isn't listed but as far as I know I backtracked while typing this so it should be right. If you don't meet the strength requirement you suffer accuracy penalties and for melee/unarmed you attack slower. Hope that helps you plan on what weapons you want. If you're struggling you may want to increase medicine skill. If I had to pick between Lockpick and Science I tend to use Lockpick; I don't think it's better but I just use it.
I put off the game for a while and might replay it (Because Fallout 3 is glitchy for my Win 7 iirc). I remember bits and pieces and a few game changers but I hope that list helps.
So re-looking at what I typed, I guess the perks I'd grab are (2) Rapid Reload/Hunter, Educated, Shotgun Surgeon/Toughness, (8) Maybe Super Slam, Finesse, Piercing Strike/Silent Running (Probably can't get Piercing Strike atm), Jury Rigging... Maaaybe Purifier because of Death Claws (Punching them sounds suicidal), (16) Weapon Handling, Maybe Paralyzing Palm or look back for Light Step, Ninja, (22) Nothing so look back, (24) Slayer. These are Vanilla perks. There's also DLC perks.
I don't know if these are plausible because of skill points per level. These are the perks I'd look into with my gameplay style (Max Luck, Guns, Unarmed). Maybe Super Slam because any chance of knocking a target unconscious makes it easy to whale on them; I can't say it's very reliable but it's nice when it happens. Maybe Paralyzing Palm too because of the same reasons as Super Slam. Both can be ignored because of certain perks you can gain from quests. One I know is the "Ranger Takedown" (see here: http://fallout.wikia.com/wiki/Ranger_Takedown). Not sure if the Takedown works on creatures, it didn't say on the Wiki.
I'd like to point 1 more thing out. With the DLC perks and the playstyle I use (try to punch everything, shotgun melee people), at Lv 2 is Light Touch, 4 is Travel Light, 26 is Tunnel Runner. You run pretty fast with Travel Light and Tunnel Runner. Light Touch isn't like Finesse and I'm too tired to understand it right now so it's best to just look up.
Finally, Leveling felt incredibly slow at 20. I think it's faster if you do the DLCs. I can't remember the name but one of the DLCs is recommended 25+. I went in with the basic gear for just basic vanilla Fallout, and it was pretty rough because of every enemy's DT. So a Level 20+ perk would take a while to get to, especially without DLCs. It might that is; New Vegas has boatloads of quests so who knows how far that'll take you.
Edit: Hunter perk only affects animals. Nightstalkers, Cazadores, Deathclaws, Fire geckos are considered Abominations.