First off welcome.
Ok, now to the questions in no particular order.
I hated the sound of the stock speakers so I swapped them out with Polk audio DB691's and 651's. They sound great and fit my style of music. You can pick up fronts and rears for around $125. If you are going with an aftermarket headunit then speakers are going to be on your list as the stock speakers are low power. Speakers are a personal preference and everyone seems to have their own favorite brand.
For a headunit with a screen it all comes down to preference and budget. You can pick up a nice Clarion vx401 with the touchscreen, Sirius ready, Ipod control with add on navigation as an option for around $330 (not including the cost of the nav unit). I am ordering the Clarion NX501 which has all of those features and nav built in. I can get it locally for $640. If you want to spend more the sky is the limit and you can easily dump 2 grand into a headunit from several manufacturers. Some people are using the Chinese made head units for the Corolla. Some are winners, some are losers. The one I bought was a loser so it went back today and I am waiting on the refund to put toward the Clarion.
Subs: The stock system has no low end and even with aftermarket speakers the low end is minimal at best. I run 2 10" Boston Acoustic G110's as they have a tight punchy response which sounds good for the punk and metal I listen to. I paid $100 each for them and push them with a Kenwood amp. I think I paid around $125 for the amp and a box will run you about $60. It is a decent budget priced system that suits me well. I am going to eventually add a 4 channel amp for my main speakers but they sound good running just off the head unit.
Headlights: This is the biggie around here as there are as many opinions as their are members. I use HIR bulbs and they work great for increasing visibility but don't have the white look that many people strive for. They are not for show but for putting massive amounts of light on the road they are unbeatable for a standard bulb. You can get 4 for around $100. I then went with Nokya 2500k 55 watt fog bulbs because I wanted yellow for my fogs as I actually use them as fog lights in fog.
The other option is HID's which are a much more expensive option. Do not use HID lights in your stock housings without have them retrofitted properly with HID projectors. Minimum for that is going to be around $750 so HID is not a cheap option if you do it properly. If you don't do it properly it is horrible for glare and blinds other drivers on the road as well as decreases your visibility. Read the sticky at the top of the forum and you will see. There are a lot of people around my area that are doing HID conversions in halogen housings and they are horrible to drive around.
Tint: That is personal preference and may be governed by the laws of your state. Some people like 35% some people like darker. The lower the percentage, the darker the tint. I am going with 5% limo tint on the rear doors and back window. Tinting the driver or passenger side windows is illegal in my state (Michigan) so if I do tint those it will be with a much lighter 35% film.
Rims are another personal preference. There is a huge rim thread here that if you are interested you can take a week off and read all of it.

I personally am looking at Rota Grids or XXR521's for my white S.
Lowering springs. Another huge selection. I am going with TRD's or Eibach's because I don't want it slammed, just a little lower and stiffer. If you are unterested in better handling also look into sway bars the multitude of braces that are available.
Tails are another choice. I personaly like the way they look stock but may eventually upgrade to LED's. A light smoke wouldn't be bad but I hate the look of blacked out lights and they are dangerous as they cut down on how visible you are to others. They are also illegal in my state.
The other stuff is easy and covered in the DIY thread. Most of it can be done and little or no cost, just time and patience.
Good luck, congrats on the new car and again, welcome aboard.