What type of RFID antenna would be best for the following applications and why?

Actually, to choose the best antenna fo rthe application you need to take a closer look at the desired process, whether to track documents, as an EAS system, or in a warehouse.

If I needed to track documents traveling through a doorway or portal, I might use a high gain, circularly polorized antenna, because ther is little control over how the document is being carried through by a person and I would need the gain to maximize sensitivity and the circular polarization because I do not know the RFID tags orientation with respect to the fixed antenna as it passes by. If I was setting up a desktop check out station, where someone "swipes’ the document as he passes, I might use a much lower gain antenna, with possible a slot design, nearfield design or other polarized antenna, so that I only read the specific document taht I place in the read zone, and not all the other nearby documents.

An EAS system, to detect when either equipment or personnel pass through a zone will probably require circularly polarized antennas, at high gain, and set up through a doorway or portal from 2 sides and probably the top as well. Possibly even multiple antennas on each side and also teh top, depending on the doorway’s width. The intent would be to "burn through" any blocking substance, such as a human, briefcase or other. Also, the circular polarization and antennas from multiple positions because the orientation and position of the tags is random and uncontrolled.

Inventory logistics in a warehouse require extensive analysis of the desired process before selecting an antenna or other parts of an RFID system. At what points do things need to be read?, cases, pallets, item level or what? How stored, stacked, shelves, etc. Moved by hand, or always by a forklift?
Dock doors, or out through a normal door? Hand scanning with a handheld RFID reader or totally automated? What are the material being tagged made of, metal, wood, plastic. cardboard? All of these things will factor in to determine the best solution

Various antennas would be used in different parts of the process. In addition, selection of the tag types to be used is also critical.

Good luck!