Income tax, social security, medicare will be the same regardless of if you do the work or an outside company like Paychex does the work. It has been a while since I did tax accounting, but I think the portion the employer pays is about 7.65% of the gross pay. Additional payroll taxes are deducted from the employee portion.
Workman's compensation differs by state, by the type of work done and by experience. Be sure you define the employee's work responsibilities in the best situation for you as long as it is accurate. For example, in one state, the cost for "janitorial services" is less than floor stripping. If you employee will be doing more than floor stripping, move him into the janitorial category.
If your company has a good safety record, your cost for workman;s comp can do down after 3 (or more) years.
Unemployment compensation also varies by state, by the fund balance in the state and by your business history. Likely cleaning service will start around 2.7 to 2.9% of payroll. But check with your state. The rate can go up or down each 6 months as the influencing factors change.
You will either have your own time to do payroll calculations, reports (probably one to state and one to federal each quarter) or expense for an outside company to do the work.
We generally figured an extra 15% for taxes and related fees.
You may also decide to provide holidays off or extra pay for holidays, vacation and such for your employee. Maybe other benefits as well.