Absolutely not level 1 with your academic experience.
You mentioned starting a family business, what about accountancy intrigues you? I would say to also look at opening (eventually) your own bookkeeping business instead of accountancy, it's definitely a family friendly option and you have the option to supplement income while building everything up by contracting as a bookkeeper for other businesses. This can be easier than finding part time or contract work as an accountant so have a think about that initial period where you're trying to build your business. For this route I'd recommend doing the ICB qualification, it's very tailored to real world experience and teaches you about the practicalities of being a bookkeeping business owner.
If you're set on accounting you need to have a think about what kind of accounting you're looking for. Some sides lend themselves to self employment or owning your own practice much better than others. Things like finance business partnering, management accounting, budgeting, cost accounting tend to lend themselves better to being an employee within industry, particularly of a bigger business. A common route for this is eventually completing CIMA.
If you want to own your own accountancy practice doing the financial accounts and tax for self employed or ltd companies I'd steer towards eventually doing ACCA.
The pain point is the following: while you're potentially able to start with ACCA or CIMA straight off the bat you cannot qualify with either within having certifiable accounting work experience. There's a write up you have to do, get it signed off by old managers etc, prove your experience and then ACCA or CIMA will approve it before you're able to call yourself chartered. If you've never worked in accountancy you potentially don't want to do all those exams without being able to get the final result.
My preferred route when talking to people interested in accountancy is to do AAT. Start at level 2 (although you can start at level 3 I think 2 provides a brilliant foundation knowledge on double entry), then level 3 and 4. All the while finding work experience and working your way up to get the necessary experience required to qualify with ACCA or CIMA which you can then complete after you finish AAT.
There is always the option of a grad scheme but I find these aren't family friendly options and rely heavily on you being near major cities a lot of the time. Long hours and the pay off is the CV and the qualification funding but it can be a slog to get there.
To summarise my ridiculously long post (sorry) I would do the following for accounting:
-Look for an entry level accounts job, ideally one that will find AAT
-Complete level 2, 3 and 4 while building your CV.
-Find an employer to fund ACCA.
-Open your own practice (you can't be a self employed accountant while studying ACCA, hence it's the last step).
If you want to open your own bookkeeping practice instead then I'd crack straight on with completing the ICB qualification!