Just check how much they charge for the privilege of them doing paye. I did supply teaching for a while at £130 a day (day to day cover) and was a ltd company as I didn't want an umbrella company taking a cut and owning my details.
Then they banned public sector freelancers from being paid as a ltd company and my agency wanted £18 a day for the privilege of administrating my pay (given they were making £60 per day for taking a phone call from one of the schools that would specifically requesting me and making a phone call to me to tell me I felt it was beyond a pisstake to then want to charge £18 a day for paying me.
In terms of how to cope with the actual work I'd say remember that whatever happens come end of day you can walk out and not take anything with you or have to think about eg. seeing that class again next every tuesday period 5 for the rest of the year.
Practice entering a fully 'zen' state of unruffleableness (made up word obviously) and letting things flow over you. Make sure you know the schools behaviour system and be endlessly positive and resilient and don't let things get to you.
If you don't like a school because of how the staff treat you or don't provide proper cover etc don't go back. The schools you do like make a point of building relationships with key people. I used to get offered permanent jobs or long term supply a lot but I knew I only wanted to be part time so held my ground and didn't allow myself to be sweet talked into nightmares.
Stick to day to day if you can get enough - longer term placements in cheap/mean schools will see you doing a ton of work you're not paid for and more hours than they agreed to with the agency. Day to day means no marking, no taking home stress and worries and so long as you have reasonable classroom management and are not the explosive type you'll be fine.
Sorry if that's jumbled or too much - head scattered after too much marking in one sitting. Good luck