The book doesn't specify, so at that point it's largely up to the DM to figure it out.

Generally speaking, I would expect NPCs to 'come with' the equipment necessary to do their jobs:

• If you have a chef who travels with you, he should have his pots and pans and knives, which in game terms boils down (ha!) to the Cook's Utensils tool set.
• A personal secretary should have his paper, ink, and quills, sealing wax, and so forth; or in other words, the Calligrapher's Supplies tool set.
• If you have a squire, the kid probably has some basic armor and a sword -- nothing fancy, just the kind of thing you'd see on any combat-equipped NPC.

The contents of a given tool set are somewhat arbitrary, but Xanathar's Guide to Everything lists out what you might expect to find in each one.

You can provide NPCs with additional gear, but it's up to the DM to decide whether they will accept it, and whether they can even take advantage of it. For example, if your squire arrived equipped with a chain shirt, he may not have the strength to handle a suit of plate armor even if you feel like throwing down the cash for it; and while you can offer him the magic longsword you just found, he may well refuse such a powerful and impossibly lavish gift.

It doesn't say either way, so it's up to the DM to decide

That is the extent of the description of these retainers, nothing further is specified about them. There are also no guidelines anywhere else that I'm aware of that go into any detail about equipment of NPCs that you start the game with.

It does seem as though the designers might not have thought this out, since as it stands, it would be up to the DM to decide what they do and do not start with. This could range from anywhere between "absolutely nothing, not even clothes" to "they have clothes, bedroll, tool sets, etc".

They wouldn't have armour or weapons, since they are defined as commoners who will not fight for you, and the statblock for commoners does not mention anything about armour (although it does mention a club, but since these commoners will not fight for you, maybe they don't have that?)

The Noble Knight's squire

On PHB, p. 136, it mentions the Variant Noble: Knight background, and mentioned the impact it may have on the Variant Feature: Retainers option:

If you wish to be a knight, choose the Retainers feature (see the sidebar) instead of the Position of Privilege feature. One of your commoner retainers is replaced by a noble who serves as your squire, aiding you in exchange for training on his or her own path to knighthood.

The emphasis above is mine. It doesn't highlight "noble", but if we assume to take this literally, the statblock for nobles starts with breastplate and a rapier, but given that the word "noble" isn't highlighted like that, it might not have meant that and may in fact just be explaining the social status of your squire.

Either way, this would be up to each individual DM to decide what such NPCs do or do not start with, and how much you are expected to pay for them (the Noble background is one of the backgrounds that supplies the most starting gold, after all...)