RexTitan wrote:

With a Pet (dog/cat) allergy, is it possible to clean a new home of
pet allergys? Are there cleaners who do this type of work?

Sure, and you'll likely need more than one.
Carpets for certain.
Curtains?
If forced air heating/cooling, the ducts are probably
a big source of allergens.

I would spend a fair part of the budget purchasing several
portable room-size HEPA filters.

Jim