What I would do right after leaving the vault is go to Megaton make sure you have enough explosive skill to disarm the bomb in the middle of town and that's a level up right away, and a bunch of caps too. Even if you pick the Little Leaguer perk and set up your specials right you'll need to use Mentats or another aid to up your explosive skill high enough. The other things I'd do right at the beginning of the game would be to speak to Moriarty who owns the saloon in Megaton.
Ask him about your dad and one of his dialogues will let you do a favour for him in exchange for information. The favour you have to do is find a junkie called Silver who lives a very short walk away from Megaton. You can kill her and steal all of her caps and meds, you'll lose Karma but she's very easy to kill and you can make the Karma back up later if you're that way inclined. Complete the Blood Ties quest from Lucy West, then do the Wasteland Survival Guide as well as both of these give you an opportunity to level up without too much trouble.
Also there are a few points of interest you might want to look up when you're in the early stages of the game. Firstly, right around the back of Megaton on the west side there's a hollowed out rock with a sniper rifle and some ammo that you can pick up right at the beginning of the game, there's a few mole rats around there when you're a low level and if you're higher it might also be guarded by some Radscorpions so be careful. Another thing you might want to check out is the crashed alien spaceship. A dead alien can be found hanging out of the cockpit of the ship grasping an alien blaster, this is one of the most powerful weapons in the game although ammo is very scarce and the gun does tend to degrade quite quickly. It's more of a special weapon and should be used very sparingly, that said when it's in perfect condition it can one shot kill almost any enemy in the game.
The last piece of help I can give you would be to check the Fallout Wiki, it's huge and it offers lots of little tips that you'll probably find really helpful. I'll start you off with links to the two things that I've just mentioned.
http://fallout.wikia.com/wiki/Hollowed_out_rock
http://fallout.wikia.com/wiki/Alien_Spaceship
How should I proceed?
I'm level 4 at the moment, I have saved Megaton, and I am in pursuit of the family, I know they are located somewhere NE of the town on the bridge.
Now I haven't done many sidequests (that I know of) should I level up before proceeding to find the family? Or should I go to Galaxy Radio first?
I don't seem to have many decent weapons, I have my trusty baseball bat, a couple of pistols and hunting rifle I got from a super mutant I clubbed to death my baseball bat?
Any advice?
Find The Family and tie up any loose side quest ends before going onto the main quest. If you need a hint I'll tell you that they're located in the subway. Evan King gives you 3 locations and two of them are an unnecessary visit and will end up just wasting your ammo and stimpaks. The train station location that he gives you is the correct area to search, if you enter the metro and follow it around you will eventually come to The Family's hideout. They are not hostile toward you so long as you are peaceful with them, if you have high speech you can convince the boy to return to Arefu, if you fail the speech challenge he'll stay with The Family.
You can also propose a deal whereby Arefu provides The Family with blood packs and in return they give protection to the villagers in Arefu. The best way to go about that side quest is to have a very high speech skill, that offers the best return in terms of Karma points. Also, if you do get The Family to give Evan King and the other villagers protection, you can go back to Arefu any time and Evan will give you a random item as a gesture of his gratefulness.
As for weapons, the hunting rifle is one of the best weapons you can have. If you travel to almost the very North Eastern area of the map you'll come to a settlement called The Republic of Dave. You'll find a safe in one of the buildings here with a special hunting rifle called Ol' Painless. It does more damage and is more accurate than the standard rifles but it uses the same ammunition and can be repaired by using other hunting rifles so I would collect as many as you can. Also this is the only place you can find Ol' Painless in the game and there is only 1 of it so if you do end up getting it make sure you look after it. With the right perks you can 1 or 2 shot a Super mutant with it.
