Howdy.
I was about in the same situation as you when I bought mine. I've made some mistakes that hopefully you will not. My main advice is to try to keep it stock. It's plenty fast as is and your life will be much easier.
When dealing with running issues there are five main concerns:
Exhaust
Air Box
Carbs
Spark
Valve Lash
Exhaust - Stock? 4 in 1? Something else? This matters for jetting. Hopefully it's stock. Check for leaks especially at the head. It's _very_ important to not have any leaks. If it is leaking, replace the gaskets. (Tip: The exhaust bolts come out easier when hot. DO NOT break them off or you are in a world of hurt.)
Air Box - We know it's stock but does it have a full rubber snorkel on back? There should be a big piece of rubber on the back that goes from the bottom to the top and openings that point towards the rear of the bike when installed. The air box also needs to be sealed. There should be foam on top of the air filter that seals it to it's opening and foam on the side doors. If it's nasty, replace it with some stick on door insulating foam strips from the hardware store.
Carbs - Should be Mikuni BS34's. They are also called CV (Constant Velocity) carbs. They look like the bare metal ones in this excellent tutorial:
http://www.mtsac.edu/~cliff/storage/gs/Mikuni_BS-CV_Carburetor_Rebuild_Tutorial.pdf It's by a forum member who is also a great guy. Read it all the way through and do what it says. The stock jets for our bikes are #115 main & #45 pilot. When stock the air screw was 1.5 turns out. Since the bike is running I doubt you'll have much trouble disassembling them but try and use a tight fitting impact driver on all the screws because they strip very easily. Getting new stainless allen screw to replace all of the philips heads is recommended. After everything is done, you'll need to do a carb sync as the _very_ last step. This cannot be skipped if you want a well running bike. If you have to replace the float bowl gaskets, the OEM ones are much better than any replacements that you can find but they are much more expensive.
Spark - Plugs are cheap, get a new set. NGK B8ES Check the plug wires for cracks especially up where they meet the coils. If they are cracked they will need to be replaced. The wires are built into the coils so it's best to replace the whole unit. If you go aftermarket, the Dyna mini's fit much better in our frame than the Dyna greens. We also have resistor plug caps on our bikes that go bad. You might want to replace those also. I've found that 2 NGK SB05F (Straight) and 2 VB05F (120 degree) work best. If you have any doubts about the wiring, you may want to do a coil power relay mod.
Valve lash - Our valves are adjusted by replacing shims with different thicknesses between the cam lobe and the valve bucket. The measuring procedure can be found in the service manual found on BassCliff's site. For something like this (and the carb sync) you may want to find a friendly local forum member to help you out because you need some speciallised tools. (And a practiced pair of eyes for your first time doesn't hurt) Some people get lucky and have a friendly dealership nearby that will swap out shims for you. If you are one of the unlucky ones, a forum member(ghostgs1) runs a shim club. You tell him what you need, he sends them and you send back the old ones plus some cash to cover his mailing costs. Another great guy.
This is a 30yo bike and it's going to need some stuff. Here is where I get my stuff.
cycleorings.com Get the oring kit (with drain orings) and the 40mm intake boot orings. (The intake orings are cheap at $4 a set so get a spare set, too) The stainless allen head screws are a nice touch too. Takes about a week to get those. Be sure and mention your bike in the paypal message in case you ordered the wrong thing. He's a forum member and a good guy that will take care of you.
z1enterprises.com - They have a lot of stuff. You are bound to be taking off the valve cover so get a couple of spare gaskets. They have exhaust gaskets, oil filters, plugs and boots, coils, wires, petcocks and more. If they have it, I buy from them. Ultra fast shipping. I sometimes get my stuff within 3 days of ordering. Great customer service as well. Highly recommended.
I don't really have a good supplier for OEM parts right now. gssuzuki.com is the cheapest but they take about 3 weeks to deliver to me. (Good luck returning stuff, too) Your local dealership will be much quicker (they will have to order parts too) but much more expensive. Terrible customer service. Caveat emptor.
I've replaced just about everything I can with stainless hardware. (All the carb screws, engine cover screws, valve cover screws, etc) boltdepot.com has the best prices but a fairly high shipping cost so make sure you order everything that you need in one shot. There are some ebay sellers that sell some kits, too.
harbor freight for the one off tools. Digital calipers are nice to have around, you'll need some really skinny ring pliers to completely dissassemble the carb slides, stuff like that.
Plenty of friendly folks around here so if you can't find it in a search, ask away.
Rob