Hi, I'm a satisfied user of Line6 wireless XDV35L.
You have to make a decision about the carrier frequency.
2.4 GHz digital systems can be used anywhere, but there is a risk of interference from a powerful WiFi signal.
This article resumes it quite well
https://www.rfvenue.com/blog/2015/01/27/what-you-need-to-know-about-2-4-ghz-wireless-microphones
VHF (170-200MHz) is robust but may suffer from interference and not benefit from the frequency agility of 2.4G, that use WiFi techniques to switch automatically frequency in order to find the less crowded.
Some UHF (470-900MHz) use this frequency agility.
Caution: there are still a number of non-digital, fixed frequency systems on the market today. They are temptingly inexpensive generally, but you really need the versatility of a multi-channel non-licensed system.
The Rode is a nice system, but it's meant to be used as a camera link, and as such a little akward to use in the context of a PA system. Form factor of the receiver is a parameter not to be neglected; a "pocket" receiver dangling at the end of a flimsy cable is not my idea of a robust tool.
Beware of products designed for podcast or digital presentation, such as Samson Stage XPD1 Presentation, which does not provide an audio output, only USB connection.
Most of the good systems are between $250 and $500.
There are indeed much cheaper systems; my experience with those is that they are not dependable and sometimes terribly hard to interface.
If you want to keep your friend, don't recommend anything that has fixed-frequency. I wouldn't recommend anything from obscure brands; stick to the good names: AKG, Shure, Sennheiser, Audio Technica, Samson, Line6.