I really love screen. It's even better if you use something like Richard Clamp's .screenrc to rebind the escape key to control+] to that you can still use control-A to go to the beginning of the line in prompts.
I also love screen -S project
Using this, you can give each screen session a name, which makes it very easy to reconnect to the right session later using screen -r project
And if you forgot which names you used, type screen -ls to get a list of all sessions inlcuding their names (and names are easier to remember than random PIDs..
Unfortunately, I bound my screen hotkey to ^Y some years ago. Before remembering it's the Emacs paste key. Ooops.
There are two other things I find useful in screen:
^]-ESC. After that, you can page back through output using vi keybindings. You can use it to do copy-paste, but I rarely need that.^]-S. After that, you can flick between the two with ^]-TAB. You don't need it that often, but it's sometimes kind of handy.