From Heathrow T5 to London Business School, Google gives me the following 3 results with similar travel times (the last option being slightly longer):

Piccadilly > Jubilee, change at Green Park for Baker St
Piccadilly > Circle/H&C, change at Hammersmith for Baker St
Piccadilly > Bakerloo, change at Piccadilly Circus for Baker St

Travel time is very similar at roughly 1h and none of these lines appear to have engineering works this weekend. I will be leaving Heathrow Saturday night in the 20:30-21:00 vicinity hopefully, so I don't anticipate rush hour crowding. Will have one small backpack and one medium-sized duffel bag with wheels that I could -- though would prefer not to, obviously -- take up and down stairs.

Which option, or what other option I haven't presented, is the best for avoiding excessively long transfer walks/hallways or staircases? (A completely step-free path is not necessary.)

*FYI, I'm not enthused by Heathrow Connect as it requires a connection from T5 and doesn't appear to be much faster than the Tube. As for HEX, it's also only running every 30 minutes this weekend so I suspect the overall travel time will be quite similar. This is also a self-funded trip so I'm trying to save on £££!