> Can I achieve this by using APs from different vendors?
Possibly, but the problems you will face in working out interoperability issues will likely far exceed whatever disadvantages there are from using one vendor. In other words, it will be easier, cheaper, and more reliable to use a single vendor's solution.
Most wireless vendors use a centralized controller and "dumb" APs to coordinate roaming, channel selection, power levels, _etc_. Because enterprise wireless products are designed to work for an entire enterprise, there's little incentive for vendors to design their systems to interoperate with others.