First of all how certain are you that this is genuine self employment, sounds like you've got one client whose paying a day rate. Albeit I don't know all the facts of the engagement but these are generally indicators of employment. Could be caught by IR35. Might be one for the end user of your services to worry about however depending on their size.
The PSC itself will pay corporation tax, likely at 19% given your expected turnover (subject to change), on its profits.
Assuming all is hunky dory, typical one man band PSC will pay themselves a salary up to the primary threshold and the rest in dividends, typically up to the higher rate band. The salary can be taken as a deduction for your PSCs profits but no deduction is available for dividends.
Tax wise it's getting harder and harder to do efficiently, but the main saving is in NIC as if done correctly you won't pay any NIC whilst still getting a credit on your record.
Also fairly common to give shares to a close family member such as a spouse so that you can take advantage of their allowances and bandings. Will depend on your personal circumstances however.
There is also an admin cost to all this, payroll, statutory accounts and filing, CT returns, etc. You'll probably want to engage an accountant to do all this given it seems you have little background as you risk getting it wrong and a good accountant will probably pay for themselves with their support around all the compliance stuff.