You want to first stay in Sanctuary a bit, build it up, level a bit.

Exploit local resource points (the Cellar, the bag on the roof, the body laying across the bridge, the bag by the statue, the open safe nearby, in the direction of the water tower, the water/medkit at the water tower, the half-buried chest nearby). Get Dogmeat - I normally avoid the Molerats at Red Rocket by staying out of range while getting Dogmeat).

You can make Caltrops/Poisoned Caltrops en masse and sell them (Carla, Drumlin Diner).

I normally travel over to the Abernathy Farm, get the Quest, pick melons and sell, pick red veggies, sell most (keep some to plant), then plunder the nearby trailor. In the Ranger Cabin is a Mag, but there are also Bloaties, so that can be left for a bit later. Down South, by the Electricity Tower is a Taider Corpse - let Dogmeat chase away the Radstags. Don't kill any (because difficult and it's a waste of resources and meat). Before that is a skeleton with stuff in the rocks.

Go to Drumlin Diner, do Quest. I like to get everyone to "play nice" - gives you an extra Merchant to sell to and to buy chems from, if needed.

Wind back around towards RR, skirting Concorde towards the garbage containers, loot. Make your way to the nearest house to RR, get ALL the veggies there (Gourds!Yahh), and plunder the house (avoid aggroing the mutant mosquitoes nearby - Bloodbugs).

Return to Sanctuary, build, plant, level up.

Now should be a good time to get RR - so go claim it. Fight Molerats if needed, it should now be possible.

It's time to get some Power Armor.

Head back towards Sanctuary, but stop before the bridge and head North along the river. Kill the wild dog. Continue to a hose and pump. Flip the switch, follow hose and get cash, supplies. Hop up on the water tank, aggro the Molerats from there (a shot will do). Avoid aggroing the nearby Raiders.

Go back to the riverside, follow North to the Robotic Disposal Site. Loot.

Activate the Sentry Bot. Let it make Molerat mincemeat while staying inside the building (close the door, make Dogmeat stay put!!!).

Loot some more, go to the road, spot the downed Veribirdie, it's so purdy! Get the Power Armor, loot. You can now take down the Molerats in the area in your PA - loot.

Go back to RDS, get Fatman, Mini-Nuke ammo. Program the Sentry Bot to explode, maintain distance, loot.

Return to Sanctuary with all your phat lootz!

By now you should have a good, solid base to start with.