Short answer. Yes, both, and both come before he takes possession. He must make an inventory of the property after notifying the owner, and give security binding himself to perform a usufructuary's obligations. These are conditions of entering upon the enjoyment, not paperwork to catch up on later.
What the law says
The usufructuary, before entering upon the enjoyment of the property, is obliged: (1) To make, after notice to the owner or his legitimate representative, an inventory of all the property, which shall contain an appraisal of the movables and a description of the condition of the immovables
Civil Code, Article 583 — Inventory and Security Come First. Read the full provision →
Why the inventory has to be made first
A usufructuary must eventually return the property in substantially the condition he received it. That obligation is unenforceable unless somebody wrote down what that condition was. Hence the inventory, and hence its timing — before entering upon the enjoyment, while the state of the property is still the owner's doing and not the usufructuary's. The article is specific about content as well: an appraisal of the movables and a description of the condition of the immovables. Movables get a value because they may be worn out or replaced; immovables get a description because the question at the end will be what changed.
The notice requirement is part of the duty
The inventory is not a document the usufructuary prepares alone and produces later. It must be made after notice to the owner or his legitimate representative, so that the owner has the opportunity to be present, to object, and to have his own view of the property's condition recorded. An inventory drawn up without that notice is worth much less when it is finally challenged, because its central weakness — that only one interested party saw the property — is exactly what the notice was meant to cure. Give the notice in a form you can later prove you gave.
What the security is actually securing
The second obligation is to give security binding himself to fulfill the obligations imposed upon him. The security does not guarantee that the property will survive; it stands behind the usufructuary's own duties — ordinary repairs, preservation, restoring the property at the end. It exists because the owner is handing over control of a valuable thing to someone he may have no other hold over, sometimes for decades. The form and amount are matters for the instrument and the circumstances, and where the deed or will creating the usufruct addresses them, that document is read first.
When the obligations can be relaxed
These duties are not immovable. The person constituting the usufruct may exempt the usufructuary from giving security, and family arrangements very often do exactly that — a will leaving a surviving spouse the enjoyment of the family home rarely demands a bond of her. So the first document to read is the instrument itself. Where no exemption appears, treat both duties as live and do them properly, because a usufructuary who took possession without inventory or security has surrendered his best evidence and given the owner a ready complaint.