The provider you choose shouldn’t make any significant difference, since tax law is tax law, regardless of who does it for you. There is no magic bullet when it comes to minimising taxes! Saying that, the tax structures they support with respect to IR35 will however make a difference.
Contractors caught by IR35 have no other option than to be paid all their income under normal PAYE, exactly the same as in permanent employment.
Contractors , outside of IR35, can structure their income using a limited company and receive income via salary and dividends, which means paying less tax, because you are not paying employers NI.
Historically, prior to the April 2016 changes to the dividend tax regime, contractors had a tax favourable advantage compared to how employees pay taxes, but that has significantly diminished. The main difference now between taxes is that hirer’s have to pay employers NI on top of their employees salaries, whereas this is not the case for contractors. But, if you choose to go down the umbrella route and channel all your earnings through one, that employers NI will be payable, out of your gross rate.
Having said that, if the contract is advertised as “inside IR35” and it is in the public sector, then the contract rate agreed should be after the employers NI and apprenticeship levy have been deducted. Agencies cannot deduct employers NI from your agreed rate.
For the limited company route you will need to start your own, which a specialist contractor accountant can help you with.
When you start comparing the umbrella companies it will come down to what’s included with their service and how much they charge. The final take home amounts will vary little in comparison with how much you are earning, so it would be advisable to choose a company that you are most comfortable with to provide a top level of service.