Decide what you really want for the long term as well as the short term.
Daily supply in a range of schools gives you fantastic experience, especially if you are willing to step up and get involved in the teaching. However, you may go through weeks with no work, and then pressured to work every day even if that's not what you want. You can end up in really dire schools. On the plus side, you only work while you are in school.
If you want the flexibility of daily, the best thing is to get on the books of two or three schools and just work for them. You will get to know the schools and the children, and you may be able to secure a reference.
The other type of supply is where you do the full job (planning, teaching, marking) for 4 - 6 weeks (or longer) where you take over a particular teacher's timetable. This is really valuable experience as it will give you a reference and show future employers that you are the real deal. You are also part of a department/team.
As for umbrella companies, I think the rules are changing on these. They are very easy to use as all your pay is in one place, and you can claim back travel and food. Given the closing of any loopholes, ask the agency, and any long-term schools, to put you on PAYE. You will need to do a tax return to make sure you get your full personal allowance.