I downloaded the game today seeing as it was on sale and I was feeling a little nostalgic over the times I played saints row 2 on my 360, I must have put hundreds of hours into the game. I heard that the pc port of saints row 2 was terrible in general but the gog version isn't too bad. I heard wrong.

I should be able to play the game fine on my laptop, (I can even play saints row 4 pretty well) but when I try to move the camera and everthing is slow and laggy. I could barely complete the first mission when you have to break out of the prison.

How do I fix the issues and should I install the gentlemen mod?

I see you already posted in the game-specific forum. I think you'll likely find your answer there.

install the gentlemen mod
even if the game runs perfectly instal it anyway the mod fixes so many problems and issues

+1 to this, the Gentlemen of the Road mod is almost essential to the game.

the game wil crash if you try to load a save made with the mod previously
and uninstalled it though so be wary of that

Even on a regular pc, not a laptop?

yes
pc sr 2 is a glitchy bug riddled piece of crap and gentlemen of the row fixes not just the bugs it also adds xbox controller overlayes and a shed load of extra options

Any more weight on the specs because it just barely runs on my system now.

not that i can tell but my systems run the game just fine
it mostly optimizes and fixes bugs and glitches

I've seen so many people complain about SR2, how it is a total bug-fest and runs like crap. All I can say is that the problems can't be universal, because it runs just fine on my system, which isn't exactly a powerhouse.

Same for me. The framerate wasn't always as high as one would expect it to be considering the dated graphics but all in all I had no trouble playing the game.

nor had i
but the mod just fixed a lot of little issues and glitches

I just installed it. I'm guessing it's going to take a while before I notice a huge difference.

I only used Saints Row Powertools (to slow the game down to roughly normal speed) and, later, a standalone vehicle handling mod (which seemed to help a bit, though the driving is still janky as hell). I still wasn't able to achieve any kind of tolerable framerate without turning most of the graphics settings way down, though (and the framerate is still not great even having done that). But it is, for the most part, quite playable, and mostly pretty fun -- though any mission involving lots of driving, especially if it's timed, can be a chore (thanks to the crappy handling).
EDIT: Removed orphaned italics tag

If I remember right it does add clothing, that's a difference. :P