Being in Calgary you will have lots of options. WRT flyfishing first: the Bow River flows right through the city with some great access. As well there is lots of access outside the city. There are a number of other excellent trout rivers/streams within easy evening or day trip distance.

Your hunting options are also pretty good. You may not need a pro guide as Alberta has what is called the Hunter Host program. In a nutshell, you pay the non-res tag cost but a close friend or family member who is an Alberta resident can take you hunting provided that NO MONEY changes hands. If your brother is an Alberta resident that would be the easiest option as a Hunter Host. There is a bit more to it than that but it is a simple proccess. You will only be able to hunt with over the counter tags so moose may not be possible as they are a draw tag in most WMU. There are some great OTC deer and elk options though. Hope this helps get you started.
Enjoy Alberta!
Jeff