Big IP APM includes limited LTM functionality for free also URL redirect in Irule?

Without a LTM license you cannot build pools with more than 1 member. If you are planning on performing local load balancing to multiple servers you will need LTM. Doing basic redirects is possible with just APM because it can be done in iRules. Load balancing to multiple pool members cannot be done with just APM. I would highly recommend reaching out to your sales team to properly size and price out the best solution for you, but it sounds like you need LTM+APM.