RFID reader and antena

I am looking for solution modules for  RFID. Specifically the RFID readers and appropriate antennas. I am working with a design that needs to follow the requirements listed below:

1) range between tag and antenna about 10-20cm

2) materials between tag and antenna: 

~5cm wood plate,

~5-10cm polyurethane or polyester

~0-5cm air

3) possible some metal bolts in PU/PE

4) tag will have to be wristband

5) the antenna max size about A5 paper sheet

To specify:
The position of tags may differ so perfect would be circular polarized antenna. The set will possibly work off-grid so would be nice to have something requiring less power. The tag will be connecting with very low frequency about 1 tag per 1-2 seconds.

I was hoping to find modules in low-frequency solutions. I am aware that distance of 10-20 cm may be a hard to get with LF/HF. I am also considering short-range UHF but the price of the module needs to be considered.

I would be grateful for your advice what module to chose.
Please let me know if there is anything else I need to clarify.