Our puppy MUST stay in a crate when nobody is home. So I need a pet/house sitter that can spend most of their time at my house. That means no house of their own and no full-time job.
No house of their own? Really? Rover's sitters all have to live permanently someplace in order to register.
Aside from that one criterion, there are probably sitters who meet your specs. However, you are going to have to ask them about their daily activities. You might find some who state in their profiles about having a full-time job or attending school full time and those you should be able to rule out. The others you are going to have to ask because I've found that many sitters have widely varying interpretations of house sitting. Some do exactly what you want, i.e., they will move into your home and spend the majority of their time there. Others may come and go because they have commitments to walk or visit other dogs. Others will only spend the overnight hours at your home (arrive at 8 pm and leave at 8 am or similar).
You can only find out by asking and stating what you are looking for in a sitter. But any sitter that cannot attend to his/her other clients is providing you with a premium service and you should expect to pay more if you do not allow them to leave the house.
Read the profiles, message those that interest you, and get the answers you need before meeting them in person. You could also call Rover and have them find you a sitter.
What area are you in ?
To owner of the puppy, Where do you live?