I'm Lv16 running around in the Vault suit putting on whatever I find for chest/arms/legs - done a few of the minutemen and brotherhood quests, almost none of main story

Is there a decent full set of armour anywhere in the game that early on? Not power armour just normal wear?

add modifications to your armor pieces. you can have pretty good stats that way. nothing beats metal armor pieces however.

The best armor you can get is what you can craft, but it requires purchasing perks (armorer).

If crafting isn't your thing, you can do the Silver Shroud quest. It's base 40 damage resist and it's the best (low level) armor I've seen. Just be packing some serious heat if you go after it. You're going to need it.

That depends on what you want from your armor. I think getting the undershirt with jeans and then layering on top of that is best early game cause you get the +1 boost to Luck. Other than that, the vault suit is good because you can upgrade it over time as well. If you continue in the main quest, you will get access to certain story character armor that will give you a unique look as well as pretty decent armor boosts. Best armor early game though is hands down whatever you can add armor pieces to. That's the easiest answer.

Rushing for ballistic weave from the railroad can help quite a bit.

Prior to modifications, I would put the armor progression to be

Vault suit

Raider armor

Leather armor

Metal armor

Combat armor

Power Armor

By 16th level, you probably have at least some pieces of PA with the basic suit. The nice thing about PA is that you not only have the PA, but also whatever other armor over your skinsuit (Vault suit, civilian garb, Long johns, Harness, Raider leathers, Road leathers, etc.) Still, I find it peculiar that while wearing waterproof, submersible PA, attacks by insignificant beasties like radroaches can still get through two layers of armor protection and inflict hit point damage on the wearer.

Until I got Ballistic Weave, I was using the Vault Suit with armour attachments.

Now, I'm using a Mk5 Ballistic Weave fortified Army Fatigues (110 DR, +1 STR & AGL), because it lets me keep using armour attachments.

Certain hats will take the weave as well. The newsboy Cap, battered fedora, and green rag hat come to mind as the ones I've found

Helmeted Cage Armor (sometimes looted from Forged)

It's not super protective, but it looks amazing.

Also you should get yourself a Hazmat Suit. It's only 5 lb to carry around but that 1000 radiation resistance can be a lifesaver.