Exploration

Grab powerful weapons early on

As soon as you leave the vault, you can get two powerful weapons early in the game: a Fat-Man (with a mini-nuke) and a Cryolator. The latter requires the help of Dogmeat so I suggest meeting him first. Also, following the second main quest will give you access to a Power Armor and a Minigun. These are precious, invaluable weapons and since they're heavy, you can store them in your personal stash (craft one or just relocate any existing container) in Sanctuary. The minigun alone is capable of shredding higher-leveled enemies you encounter.

Loot are replenished over time

You read that right. Clearing a location of valuable items and looting it clean will completely replenish over time. You'll know that it has replenished its loot when you check a previously emptied container and it has items on them. The quality and quantity of items seem to be same. Likewise, unlocked doors or containers will be locked again, terminals needed to be locked again, and enemies are also replenished. The only ones who won't respawn are the named enemies you have defeated earlier and unique/ special weapons. Ammo, chems, stimpaks, and consumables are all fair game so it's possible for you to never spend anything for ammo.

Priority Items to find and keep: Power Armors

Fallout 4 gives players a full Power Armor set early in the game and also allows you to find more (incomplete) sets scattered in various locations in the wasteland. However, unlike in the previous Fallout games where you can just equip Power Armors and stroll comfortably with them, Power Armors in Fallout 4 is not just an "equip-able" item. They need Fusion Cores to function (batteries that drain over time), they have individual parts that can be damaged over time, need to maintained/repaired, and even modified. You can keep several Power Armors and since Fusion Cores are rare, it's suggested that you keep them in your home until you really need them.

Priority Items to find and keep: Fusion Cores

As mentioned above, Fusion Cores are very rare and you must use them sparingly. You can find additional Power cores from generators in various locations in the wasteland, from vehicles in military checkpoints, or from locked containers. You don't need to carry them all the time so you can just leave them at home in your personal stash or container.

Priority Items to find and keep: Bobbleheads

Bobbleheads are collectibles that give permament boost to your specific attributes or perks. These are scattered in different locations in the wasteland. You don't need to carry them all the time, taking them to your inventory is enough to get the boost so you can just leave them at home.

Priority Items to find and keep: Publications

Similar to Bobbleheads, there are scattered unique publications that will give you additional permanent perks after reading them. Their boost takes effect immediately after picking them up and you don't need to carry them at all times. Leave them at home, preferably in a magazine rack to organize them neatly.

Don't go exploring a building/ den with a filled inventory

You have to leave ample space in your inventory so you can carry more loot from your expeditions in different locations, caves, and buildings. Dogmeat can help carry some of your stuff but take note that your containers back at home remain there and have almost infinite storage space. You can even keep your weapons, apparel, and consumables on different containers back at home. Furthermore, you can store all junks in your workshop inventory. The items you found will be scrapped automatically and stripped off their components whenever you craft or modify your equipment.

Find alternate paths

Most of the time, there are always alternate ways of opening a locked door or container. With high Intelligence and Perception and with the right perks, you can pick the lock or hack a nearby terminal to open the door or safe. Sometimes, you just need to find the key or password but that will require further exploration and sometimes killing a powerful enemy deep within the location you're exploring.

Dealing with Radiation

There will be times that you'll have to go to areas with considerable radiation. Radiation doesn't go away even if you rest or eat. Radiation is not inflicted to your body in a single amount but in a gradual, per-second basis. 1 radiation per second won't be that much but if you stayed long, you'll be in big trouble. Same goes with high radiation areas that will inflict even more radiation per second. Radiation can be removed using Radaway, an equally rare drug. You can also ask a doctor to cure your radiation in exchange for some caps.

If you really need to explore or go through a irradiated area, you need to make the necessary precautions. First, your equipment. Wearing radiation-resistant Gears will greatly reduce the effects of radiation. Next, you can also use Rad-X, another chem that will give you temporary radiation resistance. As always, make sure to save your game before going in so you can conveniently reload in case you mess something up.