Is this the resource you are using?
Illustrated Guide to Home Chemistry Experiments: All Lab, No Lecture (DIY Science) 1st Edition
by Robert Bruce Thompson (Author)
ISBN-13: 063-6920514923
ISBN-10: 0596514921
As to your question --
At first blush I would use a hotplate anytime I could.
If I could afford it - I would use one with magnetic stirring ability.
A round bottom flask and others may present problems for hot plates.
Alcohol lamps may work sometimes but the temperature capabilities are not what is needed in all cases.
Open flames are problematic when using some solvents.
As an aside, I have tried using propane plumbers soldering torch and had problems with glassware handling it.