I also am relatively new to the Solstice, having recently bought my 2007 GXP. Like you, I wanted to figure out the "biggest bang for the buck" first modifications. To me, the handling of the GXP is far better than anything else I have owned over the years. My very first car was a 1967 MG Midget, and the fastest car I have owned was a 1967 Plymouth Belvedere with a built 408 cubic inch small block MOPAR that ran a 12.39 quarter mile at 110 MPH. To me, the solstice is a great car because it has modern sports car handling and accelerates like a muscle car.
All of the previous advice is very good advice, but your specific question asked what to do "to make more power." The classic answer to more power is to optimize how the engine's air/fuel intake and combusted exhaust flows. My own study of this forum and discussions with knowledgable people indicates the following:
1) On the intake side, I believe the biggest "bottleneck" impeding performance is the design (or more precisely, the construction) of the intercooler charge pipes. If you look under your hood you will see that the "charge pipes" that run air into and out of the intercooler are round as they connect to the intercooler but are crimped partially flat where they turn toward the engine. this constriction is apparently what causes the power to actually start decreasing well before the engine reaches peak RPMs (you can see this if you look at Dyno charts of stock engines... I apologize that I am not adept enough to attach some examples). The function of the intercooler is to reduce the temperature of the air being fed into the engine, but as the engine increases RPMs, the theory is that the crimps in the charge pipes cause turbulence that impedes the flow of cooled air enough to reduce the power produced by the engine at higher RPMs. In my opinion, the best first upgrade on the intake side is a set (pair) of aftermarket charge pipes that are "mandrel bent" which eliminates the unsightly and inefficient crimps. My understanding is that the mandrel bent charge pipes don't necessarily increase power, but they prevent the loss of power that occurs at high RPMs with the stock charge pipes.
2) probably the most popular first mod on the intake side is to remove the stock air intake box and replace it with what everyone calls a "cold air intake" or as it is popularly known, a "CAI." The idea behind this mod is to have cooler "outside" air going into the engine in the beginning, but as many have pointed out, the CAI is drawing air from under the hood, not outside the engine compartment. I have seen nothing to prove one way or the other whether there is a significant gain from a CAI. I have seen a comparison of Dyno runs on a web site claiming a 2 to 4 horsepower increase from installing a particular CAI, but when I examined the charts, it seems the manufacturer picked a spot in the middle of the power curve where the CAI equipped engine did in fact show more power, but only for an instant at that one point in the curve. Along the entire curve there was very little difference, and at some points of the curve there was actually less power. If you do install a CAI, you will hear more of the turbo noises that your car makes, and many of us (me included) like this. Ultimately, it is questionable how much of an improvement a CAI gets you, and some engineers may tell you that you will actually get better flow from the "protected" air inside the stock air box. My car came with a DeJon CAI installed by a previous owner which had 2 problems: 1) it causes a CEL (Check Engine Light error message on the dashboard readouts) and 2) it connects to the engine with what I believe is the stock corrugated rubber connector hose (the corrugated rubber obviously should likely be causing more turbulence than a smooth round tube). I am replacing this CAI with a polished aluminum item from DDM works that uses smooth silicone tube connectors. If you want to keep cost down, I would say get aftermarket charge pipes and skip the CAI. I am installing the DDM CAI more for the looks than any performance gain I might hope for. It will match the finish of the DDM polished aluminum charge pipes I ordered.
3) on the exhaust side, my research on this forum indicates that the worst "bottleneck" in the exhaust system is, by far, the catalytic converter (or as it is known, the CAT). Popular solutions to this problem are either a "High Flow" CAT (I'll call it an "HFC") or a CAT delete pipe, which eliminates the CAT by replacing it with a simple empty tube. Pros and cons? Both of these solutions may be illegal due to emission regulations, but both will allow freer exhaust flow and more horsepower (around 15 to 18 horsepower if various opinions and experts are to be believed, but will require a "tune" adjustment to the software running your engine and possibly a relocation of the sensor(s) in your exhaust system. Even though this simple change leaves the stock muffler in place, your exhaust sound will be louder. You can go on You Tube to listen to various GXP exhaust sounds. IMHOP, the CAT delete systems sound too raspy and are annoying to my ear (like those "rice-burners" that run a shorty muffler with a huge, wide-mouth exhaust tip opening), but you might like them. The High Flow CAT systems have a more mellow sound, and that's what I decided to go with.
4) Parallel to the intake side, it appears to me that the most popular exhaust side mod is a "CAT back" exhaust system which may or may not give much actual performance increase depending on other factors. Those who install them like them, and there are a range of systems that offer progressively louder exhaust tones with varying degrees of mellow or loud. If I recall correctly, other posts on this forum claim that the stock exhaust system is good for something like 300+ and maybe up to 400 horsepower, again many recommending an HFC to open up the exhaust side. Your GXP already has dual exhaust outlets. Good stainless steel cat back exhaust systems generally run six to eight hundred dollars, while an HFC will cost about four hundred or so.
5) whatever else you do, you need to get an aftermarket tune. When I say aftermarket, I include the GMPP tunes available. I am currently involved in another thread started by someone asking what the differences were between the GMPP tune, the Trifecta tune, and other custom tunes. The stock "tune" in your GXP has what is commonly called a "learn-down" feature, but as I understand it (I could be wrong, but I doubt it) this just means that if you alter your physical components, the software managing your engine will use the modifications you make to reach its originally programmed power levels more efficiently, but may not increase the power your engine produces because, in effect, it doesn't want to... that is, your stock software is not programmed to increase the power, it is just programmed to maintain a certain power level.
Sorry if I have been long winded, but I wanted to explain my conclusions. I have ordered matching charge pipes and CAI from DDM works (you can get similar items from a number of other sources, some of which are powder coated mild steel in a range of colors) and a solo performance HFC thru my local garage. I have ordered the trifecta custom tune for $400 (but with a 10 % discount on sale), but Trifecta has a "Budget Tune that was apparently available from some vendors for only $200 or $250. I believe that any tune you buy will require an additional fee if you want to change it to accommodate additional modifications, so the most efficient way to spend your money is to decide which mods you think you want to make, do them, and get a tune to match. Otherwise, you will have to pay an additional tuning fee very time you decide to add a new mod. You might be able to avoid this problem by getting the HP tuners tune, but that is over $600 itself, and you will need to learn how to program the changes yourself (I think), which I did not want to deal with.
Following my own advice, I also decided to order an AEM water/meth injection kit. I was originally planning to add this later, but by installing it now (I had to stretch my budget some...) I save at least a hundred dollars, and maybe more, by not needing to retune later.
To get much more power out of my engine, I would have to start looking at turbo upgrades (significantly more expensive) and probably a high horsepower engine rebuild for reliability (even more expensive, the stock engine has many forged internal parts, but the pistons are cast, and are likely the "weak link" in the engine) or the V-8 engine swap (WAY more expensive!).
Welcome to the wonderful world of the Solstice!
Mike, near Detroit.
P.S. What Bill in BC (wspohn) said above is, I believe, quite true. You can get a very substantial performance increase from a simple tune, and leave it at that. This would probably be your biggest single "bang for your buck."