The number one thing that you want to consider are your tires. They will have the biggest impact on performance than just about anything else. For corners and running HPDE or autocross or handling in general you want to get as much rubber as you can on your car front and rear for added grip. Obviously a square setup is going to have its benefits like being able to rotate the tires for even wear and a longer lasting tire overall. Unless you decide to go with the Cortex Coilovers with the offset strut you are probably going to be running a staggered setup in order to get the most grip that you can on the front as well as the rear tires.You can run a staggered setup if you wish to do so and it would really hurt in all honesty, you just won't be able to rotate the tires so you wouldn't get as long of a life out of them as you would with tires on a square setup. Since you plan to up the power I would look at getting the most tire you can in the rear and in the front which For a street car I don't think I would like to try and go larger than something like a 285 tire in the front and the rear depends on what wheel you chose in all honesty. If I was looking for something that I could drive on the street, I would look at the Bridgestone Potenza RE-71R which is about a second faster than the MPSS depending on the course, driver etc. , but you are giving up a small amount of wet traction for the added performance in the dry as well as a tire that won't last as long. The RE-71R has a 200 tread wear rating compared the MPSS which has a 300 tread wear rating. That being said, those are tires that I would suggest so don't be afraid to go ahead and look at other tires. Just be careful, when you are looking at tires one of the 2 most important things that you are going to look for is the tires tread width as well as the choosing the correct size tire for your wheel. when a manufacturer says that this tire is a 305/35/19 all they are saying that in their lineup this is a 305 tire and each manufacturer will vary. Nittos tend to run smaller than their advertised specs and tires like the MPSS tend to run a little bit wider than their advertised specs. Tire Rack is an invaluable tool in figuring out the true width of your tires tread which afterall is the most important thing. The next thing is the width of your wheel because you can fit a 305 tire on a 9in wheel, but you are going to be hurting performance that way. On a 305 size tire ideally you will want a wheel that is 10"-12" wide with 11" being a perfect fit in order to keep the performance of the tire at the optimum level. Right now, my car is making at most 594 All motor and as is with the 285 MPSS out back I am having a hard time not braking the tires lose if I want to on my 93 tune which is only making about 565 and this is an all motor car that makes almost no power down low so you might want to think about how you are going to achieve that near 600 power mark if you really find yourself interested and involved with a corner carver.
The next thing you have to think about are the wheels in order to fit those tires on there. The hardest part about wheel selection IMO is finding an affordable wheel that is light and looks great. So far I haven't really found a great option for that and I have been looking pretty hard. Wheels are a fairly subjective item as to what you think looks great, but you have to decide if you want a square setup or if you want a staggered setup and go from there.
Suspension would be one of the most critical parts of the build and you can take days researching about and it really depends on how far you want to go. The Strut tower brace really does almost nothing for the car handling wise in all honesty. It does look cool though and is like $80 so **** it why not haha. You can go with a nice set of springs and shocks and be happy there, but if you really want to compete or beat people at your local autocross days a good set of coilovers would do the trick (IMO). Most coilovers get a bad rep because you are given an improper spring rate so you get a very harsh ride, but given someone who is familiar with the S197 chassis they would be able to set you up with the proper spring rate. I myself am a HUGE fan of Cortex Racing's suspension products. The owner Filip sets up the cars for Dean Martin & Rehagen Racing/KOHR motorsports and he certainly knows what he is doing. His Watts Link is the only Watts Link that has been approved by Ford Racing for use in the Boss 302R in IMSA Pirelli World Challenge series and you are getting a well thought out and designed kit for your car at a decent price point IMO. I do like their suspension kits, although I'm not 100% certain about their base coilover kit which includes Koni dampners and comes in a spring rate desinged for the street as well as the track. With this coilover you can also add on the offset strut mount design which will allow you to run up to a 315 size tire in the front which means MOAR GRIP!!
Xtreme-Grip Coil Over System, 2005-2014 S197 Mustang, Street
That being said, I also think the Vorshlag coilover kit is also a very good option and the Bilsteins are usually a higher quality product than what Koni produces. You may want to call them and talk to them about spring rates if you do decide to go with this kit and make sure you get something that will work for you.
Vorshlag-Bilstein TrackPro Monotube Coilover Kit (S197 Mustang) - Vorshlag LLC
One thing to look into is getting a watts link instead over a panhard bar IMO for better street manors and help prevent the rear end from kicking out on you mid corner from what I have been reading. A watts link is something that I would certainly get over a panhard bar despite its price. While it does center the axle on the car like a panhard bar, it also allows you to adjust the roll center and allows the rear axle to move in a perfectly vertical line rather than in an arc like you get with a panhard bar which will allow the improved handling characteristics over a panhard as well as create the same handling characteristics for a left and right hand turn. I prefer the Cortex Watts Link over the Whiteline unit as it is a bit lighter than the Whiteline watts link, the Whiteline Watts Link has had the a few bolts on the propeller shaft or bell crank break on them a few years ago, & as said earlier they are used on the Boss 302R's and has been an integral part of their championships and success. I just bought a Cortex Watts Link so when I get it put on I can report back how I like it over the factory panhard bar haha. While you are down there if you look at your rear axle and you see that it is covered in grease by the vent on the axle tube you might want to look into either a breather can or a catch can for the differential fluid. Cortex sells a differential breather that attaches to their kit as well. Bob's makes a pretty popular catch can for the rear differential fluid.
Another thing to look into are CC plates as one of the ways to help dial in your suspension for better times around the track is to create negative camber on the front tires of the car. Once again I think Vorshlag sells one of the best CC plates you can buy, but they are almost $500 and overkill for 99.9% of those out there. Another great option to look into are the Maximum Motorsports CC Plates which you can get with the Cortex coilovers.
Some Rear Lower Control arms would also be something on my plate to look at as well in all honesty and if you are lowering the car more than 1" some relocation brackets as well in order to get the geometry of the LCA's back into the correct position. Cortex sells both of these and are very good products. I personally have the BMR adjustable LCA's and the BMR Relocation brackets on my car and plan on keeping them on there as long as I can lol.
If coilovers really aren't your thing or out of your price range you might want to call or send a message to BMR and ask about their handling springs. They have a very nice ride, almost like stock from what I am hearing and handle amazingly well.
Here is a good video on why you should do your research as to what you want your car to do and why selecting the right parts for your car is a pretty important thing.
I'm just some guy on the internet in all honesty, it makes sense to ask those who do this stuff on a daily basis some questions and get their thoughts and opinions.