I have never used a phablet or tablet but now for some reasons I will have to. But it is on my sole discretion, what device.
I definitely would like something with free OS (Linux, PureOS, Lineage OS, etc.) It should not be too small or too large, approx. between 6 and 9 inches screen and it must be able to handle GSM data (just a WiFi is not sufficient). For me, the core functionality is a www browser working smoothly, everything else is just nice to have. Sw hacking does not represent a problem for me (Linux experience 15+ years) but hw hacking is a too big deal for me.
As it is for a business project, I do not care about the price too much, reliability is much more important.
Any recommendations, opinions, ...?
Thanks in advance!

I regret to say that I suspect it will be difficult for you to find a commercially-available tablet that's not running either IoS or Android, but I found a couple of links that might help:

https://itsfoss.com/open-source-alternatives-android/

http://www.linux-magazine.com/Online...evice-to-Linux

Have you checked out the upcoming PinePhone and PineTab?

Yes, just a couple of hours ago. It looks *very* promising, unfortunately (IMO) not yet ready for use case where reliability is a must. But I have already played with an idea to buy now something just for a (hopefully) few months until Pinephone reaches the production stage...

Nevertheless, thanks for pointing at it.

Yes that's my take as well. Likely your best bet is getting a phone that is supported by LinageOS and flashing it, that's what I've done(no gapps). I don't know if the FairPhone with Ubuntu Touch would be an option either.

Interesting reading, esp. the first one. (And it confirms that my aim becomes a hard task.)

Thanks.

So, any recommendations for a particular brand/model? (Wrt to my limitations/demands?)

Well I'd start by checking the device support list for three things.

1 Rooting Capability
2 Custom Recovery Support (I use TWRP)
3 Custom Rom Support (I've used LineageOS and SlimRom with good results)

Any of the older higher end Samsung and LG models should support those three.

I'd just look at the list of supported devices for LineageOS and choose the one that fits your bill - some phones have more than 6" screen size, phablets even more. Most tablets don't support telephony or mobile data unless it's specifically mentioned (and that would make them a phablet imo).

On a side note, I wouldn't put the GNU/Linux-based PureOS in the same basket with LineageOS; the latter is still based on AOSP, meaning Android, meaning Google, meaning not really "Free" (as in FOSS, not beer).