the 55 series is not that much different from the 50 series, its like 1-2 centimeters higher so you have a little bit bigger sidewall, which is actually better for daily driving with bumpy roads. If you want better "racing" performance then get wider tires with a lower ratio, probably 215-225 45 series but with the wider tires the lower series well actually give you about the same amount of height, but the wider width is better. And get good rubbers for the front atleast it'll help with spinning.
You might want to learn to drive your Celica a bit better, because you shouldn't need to rev to 3k+ then let the clutch go to drive normally. I used to do that too, because of being afraid the car would bog out, thats why you're spinning out.
So to answer your question, it doesn't really make much of a difference, if you don't really need new tires, then you don't really need to change them.