Since you are just starting off a career in IT, I'd suggest you seek out a job first in IT rather than pursuing any further studies (be it postgraduate or technology/company-specific certification).
You will likely find your priorities and outlook changes over time. It would be different working for an end-user than a vendor/reseller.
As for IT jobs with a "Manager" in the title; usually such a role would indicate managing people and finances/budget for a project/operations; and minding less of technology; although understanding technology (not necessarily down to the nitty-gritty) gives credibility especially in the eyes of the people that he/she manages. Managing people includes managing end-users/vendors/partners. Of course a payscale of "Manager" would be different.
As to why job advertisements ask for different product/company certifications, it boils down to the technology/products that the company that is advertising the job has bought (if they are an end-user) or are selling (if they are vendor or a product reseller/service provider).
Certainly, some company certifications would have more cachet than others and it is also in the eyes of the beholder (whether the hiring company or the job seeker). There is no magic formula that says once you have some certification you would have a specific percentage increase in pay.
But eventually such certifications would lose their value. Novell (the company that started all this certification craze) and its Certified NetWare Engineer (CNE) was much sought after in job ads in the early to mid 1990s before they basically lost market share to the Windows NT 3.51/4.0 (that's also where the MCSE became in demand). I know back in the late 1990s and early 2000s, there were a lot of "paper MCSE", people who just cram and pass the MCSE exams without real actual work experience on the products. IT resellers/service providers would get a Microsoft Solution Provider moniker and other benefits from Microsoft if they fulfill certain quotas on number of its employees with Microsoft certification.
So get out there and gain some actual IT work experience first!
In my experience vendor certifications go hand in hand with experience. If someone has certification X with 5 years experience working in job Y it will hold significantly more weight than if someone just holds the certification by itself. In fact many certifications have a pre-requisite that you have so much experience (though this isn't enforced). This is the reason you see people (solution managers/architects etc.) without certifications because they have the 'equivilent experience' which you often see quoted in job ads. Sometimes a certification might help to get you an interview but then it will be more about experience, personality and job fit.
So I don't think vendor a load of certifications would necessarily add a lot of value for you at this point other than showing it's an area of interest and you've been proactive about it.
Uni qualifications are a bit different as they open up the door to graduate schemes which a lot of the bigger companies in particular (including VMware) run and probably gives you a slightly higher entry point on the career ladder than might otherwise be the case. However it's a big investment in time when you could be getting hands on experience and earning.
So it completely depends which route you want to go down. Personally I was lucky enough to get a job where I got a lot of good experience quickly and could do certifications at the same time.