Goa has plenty of luxury resorts and hotels in the north and south. In this category you have your pick of staying at a Western chain (Marriott, Park Hyatt, or Radisson) or an Indian-owned chain that equals or exceeds U.S. standards (Taj Hotels, the Leela).
For a sense of place stay at one of the Heritage Hotels, such as Siolim House, Marbella Guest House, Casa Anjuna or Casa Britona. You'll be treated like family, because you're one of perhaps a dozen guests, and most important you'll be staying at a distinctive property unique to the area.
If you're traveling light, can carry your valuables at all times, and are ready to really rough it (no indoor plumbing), check out a beach-shack. These can be fun to stay in when you're traveling in a group, but they are not advisable for women traveling alone.