The way to get into commercial archaeology is through digging rather than more qualifications. Unless you're aiming to be a specialist in a particular area like geophys, environmental, finds etc., you'd probably be better served trying to get more practical excavation experience rather than more qualifications. In some cases, anything beyond an undergrad degree is viewed with slight suspicion. If you want to work as an excavator, then a Masters or PhD won't necessarily help you.
An MA in Museum Studies would certainly help make you an attractive candidate in a shrinking employment field. On the other hand, you'll find yourself competing with people who have both Masters-level qualifications (and above) as well as professional experience. If you can pair a Masters with some work experience (which will most probably be voluntary and unpaid), this might help. Again, a PhD isn't going to make you a more attractive candidate unless you can get some practical experience.
As to whether you'd be accepted for an archaeology PhD from a Musuem Studies Masters, this would depend on what you want to research and whether you can self-fund. The last stats I saw, pointed to the AHRC (the main source of PhD funding in Archaeology) funding only 100 competitive fully-funded PhDs across the entire UK. The chances of landing one of those is very remote, but is always worth trying if you see a project which appeals to you. Funding (or the lack of it) is something which might narrow your options. Generally, a funded PhD will be looking for someone who has a demonstrable interest and/or previous experience in the field of research which it covers - its essentially like applying for a job. A Museum Studies MA may or may not help, depending on the funded project you;re applying for.
Do you have an idea about what field you want to specialise in? If you can self-fund, then it's a matter of finding the academics who are the best to supervise you, and then convincing them that you're a good bet. I suspect that in both cases, they will be looking for some kind of link from your Masters to the research subject.
As a guide, I spent three years looking for a funded PhD in my field of archaeology. In all that time there has been one, which was won by someone with both a Masters and five years of professional experience in the specialist topic.