Well since you posted in the L36 section I'll make the assumption that you have a N/A 3.8L, so if that is true we really dont need specs on your Grand Prix.
First of the cheap upgrades would be an intake. You can make one yourself or buy and aftermarket one. There are some trade offs to be considered, so you kinda have to decide just what you want and any long term plans.
Next would be the ignition system. Probably the best thing to do there is use copper core plugs and low resistance wires. This will give you better spark and help you make better use of the air/fuel mixture and thus give you a tad bit better performance and possibly better fuel economy.
Next up would be a 180* thermostat. Not really a performance upgrade but it will help some with KR if you have any. And if you have KR then you are loosing performance by virtue of the fact that the computer will pull timing. I personally recommend the MotorRad thermostats because when they go bad, they lock into the full open state instead of being closed and causing your engine to overheat. They are a bit more pricey but worth it. Ive already benefited personally from that feature a couple years ago.
Getting a little more up in the expense range, you could get an Overkill Motorsports PCM. Thats gonna run you $160 or so, I dont remember exactly what the prices are but he is well known for his PCM tuning and he has a great reputation for his PCM's really waking up a car. Its a bit more money but I personally think its worth it.
You could also do a U-bend delete or a downpipe with the ubend delete but that too could run you $150 or more depending on what you get. I would even put that on the highly recommended list of things to do.
There may be some other suggestions out there but those are the ones off the top of my head and hopefully they help you get started without having to dig up all the specifications for your Grand Prix.