Don't overlook the value of your Lockpick skill. I like to get it up to 50 as soon as possible and the quicker you max it out the better. There are a lot of goodies (weapons, bobbleheads, ammo, ECT) just lying around if you have the right skill level. That is not to say that you should ignore everything else.
There are a few that I, personally, don't bother with (like energy weapons and big weapons) in the beginning of a game as they will not be relevent for a while. When starting out small guns can be important as most of the guns you will use for the first few hours of gameplay will likely be nothing but guns of this type. Repair is another skill that is rather important early on and throughout the game. Most of the weapons that you find early on will be in poor condition and will deteriorate rapidly.
Other than that it is usually a matter of preference. Skills like sneak, speech, melee and unarmed really come down the way you intend to play.
One last hint I will give you in the form of a spoiler. Read at your own risk:
Do not use any skill books you find. What until you reach level 4 and choose the Comprehension perk. This will allow you to gain two skill points per book as opposed to the norm which is just one. In the long run, you and your skills will benifit greatly from this. There are 13 types of skill book (324 skill books in all) in this game. If you can find them your stats will be maxed in no time.
My current playthrough has a guy with high lockpick, science, repair, and small guns skills and I haven't faced any trouble. I also made my guy super tough since I don't put a whole lot into my sneak skill so I'm seen a lot and get into lots of fights.
But basically plan ahead for what you want to see your character able to do.
Some thoughts on various character types:
General Explorer: Small Guns, Lockpick, Science, Repair. Medicine, Speech, and Sneak optional.
Diplomat: High CHA score, Speech, Barter, Small Guns, Sneak. Medicine and Science can sometimes unlock speech options as well.
Sneak Fighter: Sneak, Small Guns, Repair. Lockpick, Science and Medicine still useful even if you just mostly shoot stuff instead of exploring. Plan to get the Silent Running perk at level 10 or 12, whenever it's available. Watch your skill scores so you meet the minimum when it does become available.
Big Gunner: High STR and END, Big Guns, and get the Rock-It Launcher schematics from Moira ASAP to build a gun. Medicine useful (better Stimpak healing).
Unarmed/Melee Fighter: High STR, high Melee/Unarmed, Sneak, Medicine. Sneak might not help much in open spaces, but very nice in buildings where ranges are short. Travelling at night can help you sneak better, especially with very quiet armor like leather or recon.
Doctor (only for the daring): Science, Medicine. Could play him as a sneak fighter, but you'd be surprised how many speech options a high Science or Medicine score will grant you in the game. Speech could be useful, otherwise just use Small Guns, Lockpick, and Repair.
Keep in mind, if you're going to play a sneak fighter, remember to turn OFF your Pip-Boy light! Also, equipping heavy weapons and armor will allow you to be heard more easily. Travelling at night can be annoying, but it does allow you to much more easily avoid encounters if you must hoof it somewhere.
Like everybody said small guns is almost a must. Repair is good becuase it will save you lots of money. At first, I would choose either science or lockpick to go heavily into to. Going heavy in both is unneccassary becuase alot of chests can be opened by hacking a computer or lockpicking. Sneak just depends on your gameplay preference. I wasn't a big fan of sneaking and only found it helpful in a couple of missions. So unless you have an affinity for rogues, I wouldn't go to high in sneak. I would pick at least one other weapon type to throw a few skill points in every level. Speech was one of my favorite skills becuase it opens up at lot of unique conversation options, but is not neccessary. My first playthrough I didn't use the medicine skill and just found a bed everytime I needed healed and this wasn't a problem. My second playthrough I did raise my medicine skill and bought many stimpacks which was really nice, because I wasn't always hunting down a bed. Again this a preference. The bed I slept in the most was at the Springvale School. It always seemed like the most convient.
Yes, it's true that many of the skills in the game are rendered moot if you're just looking to complete it as quickly as possible or if you're playing only as a straight-up combat game. The only really necessary skill is some gun skill, most likely small guns since those are the most plentiful and easiest to use in the game, though melee is a cheap way to play (if you can avoid taking untoward damage from ranged weapons). Big guns and energy weapons tend to be hard to use early on, but much later in the game become some of the best weapons in the game.
Everything else depends on just how much exploring you do, or how interested you are in exploring all the facets of the game. A really high medicine skill (minimum 70) will grant you a small something in Arefu, for example. Robotics Expert is not something players would think is a great perk (though the extra damage to robots IS nice to have), but it's very entertaining if you try to use it in, say, Underworld...
Finally, you might try seeing what is the replay value of the game if you try a different character type, or play good when you were previously evil, or vice versa. If you play with the game systems, you'd be surprised how much there is to find. Enjoy!