Hi everywhereva,
One good place to start is your local library. Use their computer to log onto the Reference USA system. This will give you a list of new and mature companies.
As far as competition is concerned you have to take into account what you do verses what other VAs are doing. This could mean there is no competition as they could be offering services you don't and visa-versa
On another note, don't just rely on local work, remember working virtually allows you to contract with any business in any state or country.
Good luck!
Andrea~