Is the £200 a hard limit or can you put more in and only get credited against the first £200?
I haven't tried it but I all the sources I've found suggest you cannot deposit more than £200. What happens if you do may be down to the provider you're with.
Do I have to put away £200 every month?
No. You don’t have to put
money away every month and the amount you save into the account every
month is up to you – as long as you don’t go over £200.
You can then deposit up to £200 any time
Source: https://www.helptobuy.gov.uk/help-to-buy-isa/faq/, emphasis mine
Or will I need to open a Help to Buy ISA for the first £200 and then a regular savings ISA for the other amount I want to save?
You cannot open more than one cash ISA in a given tax year, so you will not be able to open both of these. After opening your Help To Buy ISA, your options are essentially:
a Stocks and Shares ISA in which you are investing rather than saving, introducing a certain level of risk
a split ISA, which is a cash ISA and a Help to Buy ISA in the same 'wrapper'. In this case you would save your £200 a month into the Help To Buy portion and the rest into the cash ISA portion. Not all providers of a Help To Buy ISA will offer this, so you will have to shop around. Nationwide are an example of a building society who definitely do offer this.
A split ISA seems to fit more with what you are suggesting. Rather than pay into your Cash ISA portion (or your Stocks and Shares, if you go with that) straight away, you probably want to first max out your cash in a high-interest bank account as the interest you'll get there probably exceeds what you'd get in an ISA.
There is a general "template" available here which suggests the order in which you should save your money, and Cash ISAs are fairly low down. There are more efficient ways to save before you deposit into a Cash ISA, so you should look to maximise those first. That said, there is no harm in opening a Split ISA with the intention of paying in to the Cash ISA portion of it later.