Fallout has consumed an inordinate amount of my waking hours over the past 2 weeks and I have a few tips to help as you level up your character into the twenties. I will try to keep it spoiler free for those who want to keep the mystery alive.
If you are new to Fallout one of the keys to the game is resource management, namely the weight of your inventory. In previous games you were trying to calculate which items had the best pound per cap value when you go to sell them, but with this game you salvage items for their parts and use them to build up your settlements. So the value matters less than finding items that when broken down have more crucial ingredients. If you want to see what items you are going to want look at what is required for high end upgrades on your weapons/armor/settlement and the main objects of your desire will be there. For instance "Adhesive" is a part of almost every build, so always grab it. I also recommend not carrying too many guns, pick a good short range and long range weapon and keep the others back in your base. I would alternate them depending on how I was doing on ammo.
Choosing perks when you level up will generally go with your playing style, but I recommend spending on Lockpicking early and often.
Charisma is really important when interacting with NPCs so if you want to improve your chances at talking them into paying you more or divulging secrets, find a Clean Suit and a hat that grants charisma. Wear those in town and you will beef up your charisma 3 points which will make it much easier to bend people to your will. If you find a Hazmat suit that will also make it easier to explore radiated areas with a lot less damage to your character. I carry those with me everywhere.
You will have a range of companion options as you progress and if you make one your romantic paramour you get a temporary boost in experience earned whenever you sleep with them nearby. If you do this often it can help you level up a bit quicker. Also, your companion can carry items as well so be sure to load them up so you can keep collecting, and that includes the dog. Always gather the meat from creatures you kill, and cook it for more experience. Several creatures grant useful bonuses when eaten and will help you save your Stimpaks for when you are really in danger.
I recommend that by level 10 you want to make your way to Diamond City, even if you just go there to sell items to all the vendors. When you look at the map everything to the east and south of Diamond City is where you will see the difficulty creep up. If you stay in the Northwest you should mostly contend with bugs, ghouls, and Raiders. As you step outside that area you will see more scary creatures like Radscorpions, Gunners (Raiders with better gear), and Super Mutants. You will also see enemies designated as "Legendary", they will be more difficult but will drop a special item which you will likely really want.
Whenever you establish a new settlement, make adding a recruiting signal tower one of your first additions. Everything works faster with more people. If you designate a settler as a Provisioner who establishes a supply line between settlements it will keep you from having to haul your ingredients between locations so you can build freely. I usually wait until i hit double digits to send someone away. And feel free to arm your citizens with better gear. You don't get paid great for selling a lot of weapons anyway, and they often have a crappy revolver as a default weapon.
Save often. Like every 10 minutes. You will die from lucky grenade strikes and nonsense, and the game does occasionally freeze up or glitch. If you save often you won't have to replay much if something unfortunate happens.
I hope these initial pointers are helpful to you, and good luck in the wasteland.