I played as an Argonian for my first and second playthroughs. The first I played as a good guy, the second I created a new character so I could do the 'evil' questlines e.g the Dark brotherhood and Thieves Guild.
As far as RP'ing goes, to give you some ideas my good character who I named Teekus fate made him find his way to Skyrim for him to fulfill his destiny as dragonborn. Framed for crimes he did not commit he was exiled from Black Marsh and soon found work in Cyrodill mostly meagre tasks such as farm work, and general labour in exchange for food and a bed for the night.
Eventually he found work as a assistant to a wealthy trader where he lived in relative luxury and was paid a decent amount of coin. How Teekus, although good and kind natured who always tried to help others has a foul temper which when ignited can have disastrous conseqences resulting in an argument with his employer. This led to blows and Teekus unintentionally killed his employer by punching him to the ground and cracking his head against the stone floor.
Now a wanted criminal he fled to Skyrim and was caught crossing the border and sentenced to death. After escaping he fulfilled his destiny of the Dragonborn and was forgiven by the Empire. He joined them and helped them win the civil war. Afterwards he made it his task to stop the persecution of Argonians and allow them to be treated like any other race.
He specializes in one handed weapons and uses little magic - Argonians can perform magic but are not as skilled as Elves. They are not as strong as humans and therefore I felt two handed weapons did not suit him. He is also a good blacksmith. He lives in Proudspire Manor in Solitude.
If you want an evil playthrough my other character I didn't bother with the main or civil war quests. His backstory is basically a mercenary for hire who came to Skyrim via Morrowind in search of more lucrative work. He's a kind of a nomad and never really settles in one place and is on the move to avoid enemies he has made. He does not care about anything but money and is a mean backstabber who will betray his closest allies.
He eventually settled and found companionship in the Thieves Guild.
So it depends really on if you want to play as an evil or good guy. Personally I think the Argonians come across as a peaceful race and don't ally with anyone to avoid conflicts. However they are very good at defending their homeland and can be spiteful and cruel in the case of invading Morrowind. This could have been under the instruction of a Argonian king however and normally the Argonian people wouldn't do such a thing.
The birthsign depends a lot also e.g the shadowscales. Argonians are naturally good thieves and assassins but this does not mean they have to use these skills for evil intent.
If anyone wants to have a look at my two characters I made them into presets and have various screenshots on my Steam community page here
http://steamcommunity.com/sharedfiles/filedetails/?id=231875566
