You gotta keep watching, as the show progresses and the Doctor starts to mellow and Ian and Barbara become seasoned travelers.
Yes, it's the 60's, so Barbara gets to be the damsel occasionally, but she's also the one that stands up to the Doctor the most and actually seems to think when they land somewhere new.
Especially like them in the Aztecs and the Romans.
The First Doctor's era has quickly become one of my favorites.
Partly because you can see them laying all the ground work for the next 40 years, but also because of the characters and that sense that these are a bunch of people going out into the unknown.
There's a tendency in later Who to treat the Doctor and co. as tourists, and in the Hartnel era you felt they were explorers.