Antennas don't really need substrates. For example if you look at the Ku band satellites, operating between 12 -18 GHz ,they communicate with the end user using pure metal parabolic dishes.
Similarly if you look at other extremely high performance antennas like horns for example (even in mm wave range) they are pure metal designs. No substrates used.
Nowadays antennas have become integrated with devices. Like for example our phones have antennas on the chip.
When you have to integrate the antennas the complexity in design increases. At this point you either want to fabricate it using the same technology with which you fabricate chips or make antennas that are solderable on the chip.
The substrates you want in that case are low loss , low dielectric constant substrates . As the frequency increases the dielectric constant of most insulators decreases. Low dielectric constant substrates are able to pass signals without attenuating them (either through polarization or absorbance and conversion to heat).Here are some choices
https://resources.altium.com/p/fr4
https://www.innovate-electronics.com/products/RF-Microwave/Taconic
https://rogerscorp.com/advanced-electronics-solutions/ro4000-series-laminates/ro4350b-laminates
https://www.researchgate.net/figure/1-List-of-Some-Dielectric-Materials-and-Their-Properties_tbl1_344728250
https://www.quora.com/I-need-some-idea-based-on-homemade-widely-available-unique-substrate-for-example-paper-glass-for-designing-a-microstrip-antenna-What-kind-of-substrate-can-I-use
In the following paper authors have designed a ka band antenna on rt druid 5880 substrate with a dielectric constant of 2.2 for 10ghz
https://www.researchgate.net/publication/321695202_Ka-Band_Dual-Frequency_Single-Slot_Antenna_Based_on_Substrate_Integrated_Waveguide_SIW
In this paper the authors have designed a 7ghz antenna on a paper substrate with dielectric constant of 3.2
https://www.mdpi.com/1424-8220/23/21/8996
The choice of materials will be influenced by your ability to fabricate and you'll most likely go with the same material on which you mount other components.
Let me be more concrete though. Frequencies greater than 10Ghz in consumer communication devices ,other than TV, is an upcoming technology so you may not find a standard answer.
However India has done some good work in the space of LED pcb designs. The PCB's used for LEDs are a few mm wide and are perfect for frequencies exceeding 10ghz.
With a few modifications you have a ready made patch antenna design available for cheap. Surface Mount LEDs are available in several sizes and there is a PCB for each one of them. You can get the PCB for your preferred size and build an antenna on it. No need to create your own feed network from scratch.
https://en.m.wikipedia.org/wiki/LED_lamp
Take a look at "comparison of different led modules "section for different sizes. Further these pcbs are thin and can be cut to fit in your preferred device.
Metal core PCB's would be my choice. You can check some prices here.
https://m.indiamart.com/isearch.php?s=Metal+core+pcb+blank&prdsrc=1
However metal core PCBs would only work well for unidirectional antennas as the metallic layer on the base would reflect signals. So either put antennas on either side of the pcb for omnidirectional use or use it where directivity is more important than catching signals from everywhere.
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