I only follow VoIP as a hobbyist so take the following with a grain of salt. My only faxing experience is sending a few one-page faxes over G.711u passthrough. I picked up most of this from following the VoIP Tech Chat forum at dslreports.
https://www.dslreports.com/forum/voipFor VoIP providers, t38fax.com has come up. From the website, it looks like they try to cater to fax users. There is a list of T.38 providers at voip-info.org
https://www.voip-info.org/voip-service-providers-t38/For hardware, voice gateways from "professional" suppliers (Patton, Mediatrix, Audiocodes) are supposed to be "better" than ATAs from (amateur?) suppliers (Linksys, Poly/Obihai, Grandstream). If they are, I can't really tell from the datasheets. Unfortunately, few people have the expertise and resources to perform competitive testing of multiple devices for faxing. If your chosen faxing provider has preconfigured hardware available, you should use it.
Most brands do not make any quality claims in terms of fax performance. Just "T.38" on the datasheet does not tell you the capability, the quality of the implementation or the version level. For instance, some can fax at 33600 bits/s while others can only do 14400 or 9600. It took some digging though the full user manuals to find that out.
I did hear of one brand, Netgen, that claims to be better at faxing. Their Smart ATA product line claims to have a robust T.38 implementation and faxing optimized G.711u passthrough. I haven't seen any reviews that verify these claims.
Whatever device you choose, there are settings that may help with faxing. First, you need to disable Call Waiting because that will always disrupt the fax. For T.38 settings, follow the provider's recommendations for speed, redundancy and ECM. Generally, lower speed and more redundancy should help.
For G.711u passthrough, any echo cancellation setting should be off. Fax machines have their own methods to deal with echo and the data transmission is mostly unidirectional anyways. Jitter buffer length needs to be as high as possible and any adaptive or adjustable buffer setting needs to be off. This makes sense as fax machines were designed when digital phone lines were always TDM. Dropping or repeating samples to correct buffer overruns and underruns creates audio distortion that was never considered when analog modems were designed. Dynamically changing the buffer length would be even worse.
While researching this post I just read about a T.38 faxing option on Lexmark multifunction printers! This would eliminate the analog messiness on your end. Maybe your brand of printer has a similar option available.