The type of operating system and hosting doesn’t matter much for design, but the platform is a factor. For instance, if you need a WordPress theme, the designer must work with WordPress themes and customize them in a way that a developer can feasibly code in CSS or JavaScript on the front end. If you use another CMS, the developer must work with those elements. Most designers specialize in specific platforms, so review their portfolios and experience for specific platforms before you invite them to bid on your project.
The Americans with Disabilities Act (ADA) and, if the government entities receive federal funding, the Rehabilitation Act of 1973 generally require that state and local governments provide qualified individuals with disabilities equal access to their programs, services, or activities unless doing so would fundamentally alter the nature of their programs, services, or activities or would impose an undue burden.2 One way to help meet these requirements is to ensure that government websites have accessible features for people with disabilities, using the simple steps described in this document. An agency with an inaccessible website may also meet its legal obligations by providing an alternative accessible way for citizens to use the programs or services, such as a staffed telephone information line. These alternatives, however, are unlikely to provide an equal degree of access in terms of hours of operation and the range of options and programs available.
Level AA is a little more significant, and makes sites accessible to people with a wider range of disabilities, including the most common barriers to use. It won't impact the look and feel of the site as much as Level AAA compliance, though it does include guidance on color contrast and error identification. Most businesses should be aiming for Level AA conformity, and it appears to reflect the level of accessibility the DOJ expects. 

As a result, most ADA suits are brought by a small number of private plaintiffs who view themselves as champions of the disabled. For the ADA to yield its promise of equal access for the disabled, it may indeed be necessary and desirable for committed individuals to bring serial litigation advancing the time when public accommodations will be compliant with the ADA."[57]

Olmstead v. L.C.[65] was a case before the United States Supreme Court in 1999. The two plaintiffs L.C. and E.W. were institutionalized in Georgia for diagnosed mental retardation and schizophrenia. Clinical assessments by the state determined that the plaintiffs could be appropriately treated in a community setting rather than the state institution. The plaintiffs sued the state of Georgia and the institution for being inappropriately treated and housed in the institutional setting rather than being treated in one of the state's community based treatment facilities.
Talk to your web designer about other techniques that will make your site more user-friendly for people with disabilities. Worried that’s not in your budget? Consider the fact that DOJ fines start at $75,000. And it's still yet to be determined if a non-compliant website is liable for one fine or will be charge per page for each violation. As the recent lawsuits illustrate, though, settlements quickly add up into the millions.