Double Transactional Replication (e.g. Two report servers)
Is it a good plan to use SQL Server Transactional Replication from
  server one to server two then another from server two to server three?
  Most of us DBAs here are advise against it.


I have done this before because that was the best design we could come with to meet business requirements.  Biggest issues with this design, if you are to make any changes to any publication/article you will first have to 


Remove the subscription from server two to server three
Make changes in publication/article in server one
Reinitialize and resync between server one and server two
Once sync is completed, add back subscription from server two to server three
Reinitialize and resync between server two and server three (There is a way to avoid this step. See this question and answer)



  Are two subscriptions from the production server a big hit?


Depends on two things:


Location of the distribution database
Push vs Pull subscription


If you are using the same publication for all subscribers (two in your case) the workload on publisher database/server does not increase provided your distribution database is not in the same server as publisher databases. Log reader will read the publication database's transaction log once and add the replicated transactions in the distribution database. Distribution agent will read transactions from the distribution database and apply in the subscription databases.