Edit: Saw the maple leafs logo so assumed you were from Canada. Excuse the comparisons. Where you from mate?
South Sydney or St George Illawarra would be the logical choices for heritage and history. South's have won the most competitions and the Dragon's big red V is the world's most iconic Rugby League Jersey.
They are also (possibly along with Parra) the most supported clubs in a national and international diaspora sense.
The Dragons are a joint venture between St. George and the Illawarra Steelers (an industrial region to the south of Sydney...Hamilton to Toronto would be an apt comparison). St George brought history and success to to the table and the Steelers brought a massive junior base and a non-Sydney Rugby League heartland.
Souths on other hand are historically an inner city working class club traditionally based in a now largely gentrified part of town (think cabbagetown). The large indigenous population around redfern mean South Sydney have and always will be regarded as being linked to the aboriginal community.
Steer clear of the Roosters. They are Souths richer, less successful cousins from a historically wealthier part of town. They are famously heartless and poorly supported despite the $$$.
Newcastle is a non-Sydney heartland club fallen on some tough times but will rise again.
Parramatta are also a big brand and widely considered to be sleeping giants.
Steer clear of any club that aligned with super league. 22 years on, it is still an unacceptable and frankly embarrassing stain on any club's history. It is the hallmark of a heartless entity.
Good luck and happy choosing.