Whatever you end up watching, Mariolee, I can't recommend certain episodes highly enough. In no particular order...
Any Steven Moffat episode (The Empty Child two-parter, The Girl in the Fireplace, Blink, Silence in the Library two-parter), particularly as they set up a lot of themes for Moffat's era.
Any Paul Cornell episode (Father's Day, Human Nature two-parter)
Midnight
The Waters of Mars
The End of the World
Gridlock
Dalek
The Impossible Planet two-parter
The Fires of Pompeii
I've left some more controversial ones that I personally love off the list.
There's a different sense of tone and style than the Moffat era (more comic book, IMO), sure, but any of these are top-notch episodes of television that are well worth your time.
Also, watch some Eccleston stuff. The man's wonderful.