Like some of the other comments, if you really need a DE then maybe give XFCE or LXQt a try. The distro itself won't matter too much in your scenario.
I do have an old laptop that has run Debian/Ubuntu + Gnome fine, not at all fast but usable for my needs. Mines has 4 GB RAM, get the feeling that going under 4 GB may be a bit much.
Otherwise Linux is perfectly usable without a DE if you're willing to stick to the terminal for all your usage.