My understanding is a ship is a ship. Where you purchase it is not really a factor as to how the ships stats are. The type of ship you fly depends on how much cash you have to spend on one, and what your primary purpose is. Combat, trade, exploration, or a blend. In the older elites, as I recall, certain factions would sell certain ship types. Such as an Imperial Clipper would not be sold by an Independent system. Go to a high tech Empire system, and you may find one. I haven't really focused on that in ED.. so haven't noticed if it remains true.
The hauler, type-6 etc pretty much means you are a merchant type. You won't be effective at all in combat situations. The starter ship isn't bad for light combat and very limited trade/courier type missions. Go viper if you like a fast ship decent at combat. I personally enjoy the cobra most at the moment. Its a nice blend of combat capability, speed, and semi-decent cargo space. The next step up, the asp explorer is far more costly, but a decent hybrid ship. Loads of cargo space, and hefty combat capability. Though it is nowhere as agile as the cobra.
Remember a stock cobra is far less capable than a cobra decked out in higher rank gear and weaponry. A well equipped cobra can make mincemeat out of a stock Asp. What is great about this game though, is pilot skill does matter. A well piloted stock cobra is still a serious threat to a larger ship, for example.
To be more in tune with your question however... where you do missions, determines how a faction sees you. Example.. if you like Empire, do missions in Empire space. You can mix and match with other factions as you travel around. I don't think anyone quite knows the underlying faction mechanics as of yet, they may not be fine tuned yet for Gamma but should be at release. My best guess would be.. if you do missions for an opposing faction, it may have some impact on your reputation. You don't want to do military hits against Empire authority ships for a Federation system, for example.. if you consider yourself Empire.
One cool thing I'd like to see is with faction increases: it would be nice to obtain 'faction colors' to apply to your ship. It could be sort of a badge indicating your seniority in a given faction. This is above and beyond whatever your overall trade/explore/combat rank is.
I look forward to seeing many more ship options. The available complement seems very small.. though I can't complain. The quality of what is in the game is wonderful. The ship modelling, cockpits, overall design. I can absolutely understand why the developers had to make certain choices to ensure they got the game out the door. It leaves a LOT of space for future updates.
Hopefully this helps a bit..