Hiring employees whether they are regular employees 1099 contractors or temp agency does NOT make your company an LLC. Filing articles of incorporation with the State makes the company and LLC whether you do or do not every hire an employee.
You really should talk to an accountant and ask them to refer you to a small business attorney. Yes, those will cost you up front, but if you don't know the basics of an LLC, it will be money WELL spent.
Oh, and kudos for wanting to go about hiring employees above board. I have done that from the start and never have to look over my shoulder. It is a royal pain, the government doesn't make it easy, but I'd still tell you it is the wise move.
Now, to your original question: I talked with a couple of temp agencies a couple of years ago. My thought was I'd have my selected employee work through them so they would handle all of the paperwork and tax stuff. It sounded like a good option, but I decided to just do it myself. You just need to report Federal, State, Local withholding quarterly; annual reconciliation for the withholdings you already reported; annual W2; unemployment (if you pay above the threshold); worker's compensation; and now possible ACA paperwork depending on number of employees and hours per week they work.