What magic items can a Shield Guardian use?

Question

Shield Guardians are large constructs with an intelligence of 7. They can be commanded by the owner of their Master’s Amulet.

Apart from weapons and armor, can a Shield Guardian essentially use any magic item? Could they wield wands? Rings? Masks?

Are there any particular limitations for Constructs using magic items?

Answer 1

There are no general restrictions on Shield Guardians using magic items

In Chapter 7 of the DMG, in the section called "Magic Items" the book lays out the categories and general rules for using each category of magic item (I'm not going to list them all here).

There are some limitations listed (rings must be able to be worn on an applicable digit, and you must be able to read a scroll, for examples), but none of them restrict the use of magic items by Shield Guardians or constructs in general.

Specific restrictions will apply (eg spellcasting attunement)

However, many magic items have restrictions beyond their general rule so you must check with each item you want the guardian to use. For example, since shield guardians are not spellcasters they will not be able to attune to (or use) items that require the user to be able to cast spells. Many cases may require your DM to make a call about whether the particular item can be used.

Note that any items attuned to it count as attuned to your PC (in AL)

Any item attuned to an NPC under your control (such as, but not limited to, familiars, beast companions, simulacrums, conjured creatures, hirelings, lickspittles, etc.) counts against both your character’s limit of three attuned items and the character’s permanent magic item count.

This rule doesn’t imply that such creatures have the ability to attune to magic items. Whether or not a mindless undead creature—for example—can attune to something is subject to DM discretion. (DDAL FAQ v 7.1 p. 8)

So, make sure you are abiding by your 3 item attunement limit.

Answer 2

Items that require a spell caster to attune aren't usable

The Monster Manual (p. 271) doesn't list spellcasting as an attribute of this creature, so any magic item that requires attunement by a spell caster would not be usable. If the shield guardian had spellcasting as a trait, it would be listed. That trait isn't listed.

A monster with the innate ability to cast spells has the Innate Spellcasting special trait.

A monster with the Spellcasting class featue has a spellcaster level and slots. (MM p. 10)

Beyond that, there does not appear to be any restriction. Check the item description of a given magic item for any other restrictions.