You need to ask yourself a couple of questions:
1. What kind of music do I listen to 80% of the time.
2. What do I want the tC to become?
3. How much do I want to spend/time on developing the tC
4. How much do I want to spend financially?
5. Personal know How/DIY
1. and 2. are very important. Depending on the type of music you listen to will dictate which components, speakers, HU, amps, ect. to install. If you listen to classics, classical, rock, instrumentations, then you will need better Highs and mids with a 4-channel amp to power them vs. HU power for clarity. If soul, r&b, rhythm, bass are you methods then more focus and Highs and Lows with second thought to mids will be the better solution. I could discuss this in more depth, but that requires time.
Next, what do you want the tC to be. Do you want a roadster to hug the curves and smoke cars on the strip with tunes as accessory or do you want a cruiser to take out on the town with friends with tunes to please everyone in the car. Do you want bells and whistles or do you want quality.
After answering these questions you can develop a timeline and budget. Based on personal know how or Do it Yourself you can save money but increase time spent on install.
Personally, my timeline is a month. First, I just installed an alarm and window tint. Less people who know where you live and what you have the better. Next, the system. I'm going for aesthetics and quality, thus more money. GPS,DVD, XM and I-Pod ready HU with pre out 8 volt current to a 4 channel amp will give me quality and appeal. This will be install last due to the price tag. A mono block amp will be my choice for the lows, with a 12" high quality sub for bass to be modded in the hatch/wheel well. I do not need much bass, the 12” will be plenty. Pics will be posted later. Component speakers with tweeters will be installed (front and back) at the same time as the other amp and sub for sound quality (can test and teak them at once). This I have done and the doors come off like a charm. Doorsills are easy with wire tracks in the frame. Thus, I do my own install and save 400 bills. I have removed the middle console where the HU is and it comes out easily. Also, a standard Toyota wiring harness works like a charm. Just follow the directions zoltiz has posted, just do a search. If you want more descriptions let me know as I will post pics and show more of the modding.
Is this system needed, no. But for me it is. I like the look of a touch screen HU instead of a flip up, and the tC is an easy machine to work on. I like GPS and I need security, so a form of Lowjack is installed with it. To me, it sounds 100% better, but I know what I like and need. I also want a cruzier the can get up and run, but still be able to take a lady to the show. Thus springs and front strut bar also work but will be installed next month. Ah, time frames and waiting. My suggestion is look at the big picture and build accordingly. Do not rush into a new system. For a majority of people, the stock system is perfect. Let me know if you want a more indepth response. Alpman also has some great post.