I would personally use Debian as my first choice then use Ubuntu if there is a reason to use it over Debian. For example Ubuntu will often integrate drivers for new devices faster than Debian. But if you are dealing with hardware released more 1 year ago, I wouldn’t worry about that. Also, some applications will specifically call out Ubuntu as their supported distro.

If your Internet connection is 1g or slower just about any desktop built in the last 10 years should be fast enough. The critical thing is having a good network card. Intel is generally very reliable for network cards and you can get used ones on eBay for not to much.