You should start with older stuff, honestly. Matt Smith (which is the one I assume she showed you) was extremely goofy and the writing, though fun, had a lot of nonsense in it.
Christopher Eccleston spent some time as the Doctor years ago, and he did it damn well. The episodes were solid and didn't rely on you being a mega-fan to make sense of it. That carries into David Tennant's years as the Doctor, as well.
Starting at the beginning is way better.
Also, the Angels are fucking awesome. Some of my favorite villains in television.
As a side-note, you didn't have Rose Tyler as your first Companion and I feel bad for you. She was such a fun one.