From levels 11 to 20, focus on unlocking crafting. Upgrading your armor, weapons, and power armor will do more than weapon damage perks. Use Power Armor based on how many cores you obtain, and look to upgrade the Pipe rifle. You can even get .50 caliber rounds and make it a deadly, cheap rifle or automatic weapon until later levels.
Here’s a list of the best perks to select from levels 11 to 20 with the Survival Build Guide in Fallout 4:
Level 11 – Scrapper
Level 12 – Locksmith 2
Level 13 – Science
Level 14 – Gun Nut 2
Level 15 – Armorer 2
Level 16 – Science 2
Level 17 – Lone Wanderer 2
Level 18 – Locksmith 3
Level 19 – Local Leader 2
Level 20 – Lead Belly