I know that there are some champions who are better solo-top than others, such as Shen because he can heal himself and he has good survivability, but what else decides if a champion is primed for solo top? I have seen other champs such as Teemo or Talon do really well in this lane, but I still don't understand the decision.
You need Lifesteal. A "getaway" technique, for example Talon, can easily use his E or even his ult to dash away. Teemo can also use his speed.
Most top champions have good sustain,have a way to escape in difficult situations such as ganks, and also has the skill set to be able to defend your Attack Damage Carry and your Ability Power Carry. For example, Nasus has great sustain with his passive, and his w can let him escape out of tough situations. Teemo has the ability to blind and escape. With the blind Teemo can stop basic attack reliant champions (ex. Tryndamere or other Attack Damage Carries) from damaging your allies.