Just like the others said, if it's a carry gun then keep the factory connector and just polish the internals, since it's a full size glock and your first semi-auto handgun I just assumed it would be a range/self defense gun and not a carry gun. No need to take it to a shadetree smith at the gun show, if your in the Jackson area bring it by my house and I will install the connector free of charge (you supply it or you can buy one off me, I have quite a few on hand) and polish the internals for $10 (just because it's takes some time to polish everything just right). There are various other things you can do to enhance the trigger but those are the two most common modifications and generally satisfy anyone who doesn't shoot in competitions with their Glock. I can also install a set screw for overtravel adjustment in your factory trigger housing, radius the safety plunger or install a titanium safety plunger (they are already modified correctly), etc. I'm a Glock Certified Armorer and have been building custom Glocks for about 3 years now.
Total for installing the 3.5lb connector, polishing the internals, and the cost of the connector would be $24. I would suggest doing that first and seeing if that improves things enough to your satisfaction before you try anything else. If your interested shoot me a pm. Turn around time is an hour from when you drop it off (I have done well over a 100 of these so it doesn't take me long).