Bob and others have said it right, traction is #1. Get some wide grippy tires and go from there. My biggest complaint about our cars is the traction (it's something the HC guys know all about) on the street. Sure you can throw some Slicks\DRs on there for the track but for a daily driver that's where the problems come in. I have 315 DWS06s on an 11" wheel and I can easily break them loose with my 392. It's even worse now with a tune.
Once you get some grip, look at getting a tune. It cleans up the slop from the factory setup. I got mine from Jay Greene and I'm really happy. He didn't need a wideband AFR setup where other tuners did. I'm not a tuner so I can't speak to if you need one or not. I made a post about how excited I was and another tuner (Satera Turning) was saying that you need a wideband to properly tune the car and it devolved into a major thing between Jay and Jeremy. I'm not sure if it was due to me deciding not to go with him and going with Jay instead or what but I'm happy with mine.
After that then you're looking at a cam, headers, and E85. At that point you've hit your peak without doing massive engine upgrades and adding FI. You need to upgrade the internals for FI. Yes you can run it and others have ran it without forging the pistons and rods but that's a ticking timebomb and you need to be willing to accept the risk that the engine may be damaged if you don't forge them.
And tires + wheels is only a small part of the traction equation. Some things you can't help with a factory car... like weight bias. However, you can work to better transfer the weight with softer springs and a modified rear suspension setup.
Traction loss happens when too much force is applied to the tire without enough counter-force applied to hold the tire down. Rotational velocity of the tire wants to lift the tire off the pavement. Adding wider tires increases the car's footprint, which actually lessens the down pressure onto the surface. It's why tank tracks are wide, and many 50+ ton tanks can run over a person's legs without pancaking them as the weight of the vehicle is spread across the width and length of the track. They're needed to keep from getting bogged down in soft surfaces. Similarly, a bicycle sized tire on a modern car would produce an enormous amount of down pressure, but the drawback is when traction is lost, you'd instantly lose control of the car. Thus, you have to achieve a balance between width and desired down pressure in order to maintain performance without sacrificing control.
Simply adding wider wheels and tires can do the exact opposite of increase traction. This is especially true if you achieve that fitment by using wheel spacers, as it moves the contact point further outboard of the car's center of gravity. To increase traction, you have to increase the vertical force pushing down on the tires. This is done by effecting efficient weight transfer onto the tires via a soft suspension that allows the car to squat down over the rear diff. The other side of the coin is straight line control. Wheels that float (aka burnout) will cause the car to turn slightly to the left. This is magnified if the car is under partial traction and moving forward. Lateral slip reduces grip. Thus, you need a positive solid bite at launch to set the grip, but then you need the rear geometry optimized to hold it, or you'll still break out again anyway. Things like sway bars and IRS K members can strengthen the rear geometry to become more rigid and more effectively transmit vertical momentum into positive intertia.
Simply slapping big tires on a car might increase traction a little bit. For example, if a big tire can potentially increase traction by 20%, without the suspension upgrades it might only add 5%. You can get away with tires only upgrades on relatively low power cars like Scat Packs, Mustang GTs, and so on. But cars that are running north of 700hp, just doing the tires isn't going to solve a traction problem. You have to spend some serious money and put a track focused performance suspension arrangement on to be able to launch a 305 or 315 with precision. The stock suspension in a Redeye or even an SS isn't exactly a track focused suspension. It's a decent middle ground between a road and track suspension... but if someone is serious about racing, that stuff has got to go.