Improvement based investigators like Lola and Lily are tricky in that they can be shut down if improvement cities are blocked by tough monsters, or if you draw them as replacements mid way through a game and don't have time to go improve skills.

Although it is satisfying to get Lily to the Antartica board and meditate on top the mountain until she has +2 in everything.

Of course, Lola's ability means that she doesn't care if a certain city is blocked - she can improve the skill of her choice in any city at the cost of an action,

I like to include Charlie Kane when playing solo. He's easy to add to get to a 4th character requiring very little attention once he's in a good city (I like Tokyo). I will also use him when playing with odd numbers of newer players to hit an even number, then we control him as a group.

Other than him, I usually deal out a few to each player to pick from.