Xfce Terminal Emulator, Konsole, and Gnome Terminal are good terminal emulators, and all are going to have tabs and keyboard shortcuts. The decision is mainly going to come down to which toolkit you like and which dependencies you can live with.
Xfce Terminal is a personal favorite of mine. It's simpler then the other two, but it's mainly missing profiles, which the other two have, which I don't use. It uses the GTK+ widget toolkit, and it has some dependencies to Xfce.
Konsole is from the KDE project, and like all things KDE, it has tons of knobs to tweak. At one time it had the distinction of being the fastest terminal emulator due to some intelligence code which cut down on the amount of text written to the screen while scrolling. It relies on the QT widget toolkit, and has dependencies to KDE.
Gnome Terminal served as the basis for Xfce Terminal, so the preferences look the similar to Xfce Terminal. The biggest difference is the inclusion of profiles. I'm not sure what difference they would make, since I don't use them. It's based on GTK+, and it has dependencies to Gnome.
I'm sure there are more term emulators out there that are lighter weight, but these are just the ones I'm most familiar with and the ones most Terminal.app like.
xterm
supports copy/paste, or at least it should. Are you using the wrong hotkey? Shift+insert should be paste by default – Michael Mrozek Jan 18 '11 at 21:39