Once you have established residence and have the required ID (utility bills, council tax, etc.) for opening an account, you may open a fully funded ISA at anytime during the UK tax year. It will not be pro-rated for partial yearly residence.
What I'm not sure of is the need for a National Insurance Number. ISA's require strict notification to HMRC (since they're tax free). I've not changed providers for years. In the past, it was required; as to now, I've no idea.
Once you open an ISA with a provider, you must stay with that provider for the remainder of the tax year. In other words, you can't put £10,000 with one provider and £5,000 with a different provider at the same time within the same tax year.
It sounds as if you are well aware of the major pitfalls of a stocks and shares ISA. You may have one, and there's nothing wrong (illegal) about it, but the IRS reporting requirements are horrendous. Cash ISA's are simple and straightforward to report to the IRS.