Hi Cade. I agree most of the information there.
There are a few things you need to take note of:
1. I'm sure some textbook would tell you supressor T cell exit. In the last 30 year there has been a major debate over the existance of these supressor T cells, and we don't knwo whether they really exist or not.
2. Remember, only the cytotoxic T cell from the three cells you have mention actually "produce toxic substances that destroy cells that have been invaded by virus."
3. T cells also help B cells to recoginse antigen.
4. You said "T cells would remain in thymus till come in contact with antigen"
This is incorrect. T cells mature and gain their receptor specificity in the thymus. After selection, they leave the thymus and circulate around the body. They make contact with antigen in the lymph nodes, not in the thymus.