Hello,
we are currently running on 2.6.0.beta1 and now want to upgrade to the latest version, but a stable one. As 2.6.0 is an old version, is there anything we need to worry about? Of course we will do a backup first, but maybe there are some hints 
There is little chance that the OS of your VM is supported. I recommend that you Move a Discourse site to another VPS with rsync, skipping the database files, build the new container and then restore a backup from the existing site.
Actually, I would probably recommend that you run a fresh discourse-setup rather than using your existing app.yml and copy over the SMTP settings and such. There have been some changes there too.
Pretending for a minute that you perform OS upgrades on the VM to get it up to date, there have also been at least two postgres upgrades since then. Trying to upgrade in place will not go well. If you try, and it fails, I won’t say “I told you so,” but I won’t say anything else, either.
Many thanks for your answer. As we also need to move to a new server, the original plan was to migrate the old discourse first to the new server and then do the update.
Would you still recommend to install new discourse?
Moving to the new server is much safer since you don’t need to change the old server until the new one is working!
What I would do is follow the rsync guide, excluding postgres_*. Then I’d rename app.yml and run ./discourse-setup --skip-connection-test (because the DNS won’t be pointing to the new server yet. Then restore the backup. You can (usually) test that the new server works by changing your local DNS to point to it, but worst case, you just change the DNS and if it’s a disaster you change the DNS back. (If it’s digital ocean or something else with a floating-ip that can be pointed to multiple VMs then you can just re-point than and not fuss with DNS.
I’ve done this about 10 times in the past couple of months. If you’d rather not do it yourself, I’m available.