What is the strongest fixed location equipment you can obtain at Level 1?

Thus far the best I have found via playtesting are as follows:

1-Handed

• Elven Sword, 12 base damage, found in the Dragonsreach Jarl's Quarters in a locked display case.
• Scimitar, 12 base damage, obtained by killing a Corsair on the Dainty Sload (boat northeast of Solitude).
• Dawnguard Waraxe, 11 base damage, found on the roof of Fort Dawnguard.

2-Handed

• Elven Warhammer, 22 base damage, found in Jorrvaskr in a locked display case.
• Dawnguard Warhammer, 21 base damage, found on the roof of Fort Dawnguard.

Archery

• Elven Bow, 13 base damage, found in Jorrvaskr in a locked display case.
• Ebony Bow, 17 base damage, sold by Falas Selvayan at the Ramshackle Trading Post in Solstheim, possibly equipped.
• Glass Bow of the Stag Prince, 16 base damage, sold by Falas Selvayan at the Ramshackle Trading Post in Solstheim, possibly equipped.
• Crossbow, 19 base damage, found on the roof of Fort Dawnguard, slow reload speed, 50% knockback, very different firing arc from longbows.

Heavy Armor

• Bonemold Armor and Shield, 73 base armor (+21 w/shield)(set), found on a dead Redoran Guard (along with Elven Bow and Sword).
• Dwarven Armor pieces, 78 base armor (+26 w/shield)(set), found in various Dwarven Ruins, full set in Nchuand-Zel but may be difficult to obtain and may require some quest advancement.
• Dawnguard Heavy Armor, 104 base armor (+26 w/shield)(set), given upon siding with the Dawnguard early in their questline, shield is found on the roof of Fort Dawnguard.

Light Armor

• Penitus Oculatus Armor, 51 base armor (set), kill the Penitus Oculatus agent in Dragon Bridge, bonus points for being able to equip a Circlet with the helm.
• Dawnguard Armor, 61 base armor (set), several pieces found in and around Fort Dawnguard, I think you need to progress through the questline to get the chestpiece though.
• Diadem of the Savant, 7 base armor (head), found outside Froki's Shack, Circlet.

Though this might not be helpful to you, there is a bound bow spell obtainable in Fort Amol Prison. The bound bow is a daedric bow (or at least very close to it), with free daedric arrows.

Shrouded Armor set, just start the Dark Brotherhood questline via Aretino in Windhelm, requires two kills (grelod and one of the 3 captives both of which pose no threats), the armor is basically a handout from astrid

Steps:

1 Finish unbound quest

2 Go to Windhelm via carriage or steal a horse in Whiterun Lockpick Aretino residence in Windhelm

3 Talk to Aretino

4 Go to Riften

5 Kill Grelod in Honorhall Orphanage, no need to sneak, no bounty is given

6 Return to Windhelm and talk to Aretino

7 Find a bed and sleep

8 Astrid should have abducted you

9 Kill one target (all are 1 hit kill and non hostile)

10 Talk to Astrid

11 Fast travel to Whiterun, hire a carriage or steal a horse, go to Falkreath

12 Locate the Dark Brotherhood Sanctuary (marked location)

13 Talk to Astrid

She should give you the Shrouded Armor set (Light Armor, 4 pcs set)