I did some research on different inexpensive RFID readers and I ended up building my project around this one
https://www.parallax.com/product/28340
I also bought these tags:
https://www.parallax.com/product/28161
The problem is that whenever I get close with the tags, sometimes it doesn't read them at all, other times it takes 1-10 seconds to read it.
I use this code to test it on my ubuntu (I tested it on a raspberry pi as well, same issue): http://theatticlight.net/posts/Using-a-Parallax-RFID-reader-on-the-Raspberry-PI/
I am not sure if this is a problem with my reader or something else I am doing wrong.
Would a 13MHz reader/tag have faster reading speeds? Is this problem related to the specific antenna of the module?