Can I just pick a series based on the actor?

Yeah. That's the deal with Doctor Who. Some episodes from the earliest actors to play The Doctor are lost anyway.

The first episode with each new actor is meant to be a starting point for new fans.

Matt Smith's Doctor is a great choice.

Be aware though, that much like different series of Star Trek have different vibes, different seasons of Doctor Who do, as well.

Matt Smith's Doctor Who is as often borderline fairytale fantasy as science fiction. (Though with enough extreme patience, and a little bit of generosity, one could argue that most unexplained bits get plausibly explained later.)

• Eccleston'a era is more distopian.
• Tennant's era has more retro futuristic adventure.
• Smith: Fairy tales in space and time
• Capaldi's era is rock and roll scifi.
• Whitaker's era returns to the shows roots of exploring history.
• Gatwa: Fairy tales, again, but sexier

And, because I'm old:

• Peter Cushing (yes. That one.): Scifi Horror
• Hartnell: Exploring history.
• Troughton: Morality Tales in Space and Time.
• Pertwee: Scifi Horror
• Tom Baker: Shakespeare in Space and Time
• Atkinson: Dark Comedy in Space and Time
• Davidson: Hardy Boys Mysteries in Space and Time
• Colin Baker: Rock Opera in Space and Time
• McCoy: The Twilight Zone
• McGann: Shakespeare in Space and Time, revisited, with a touch of rock opera.

Have fun!