Hi Kate, congrats on getting a pointy! Homechecks are fine. Someone from the charity will visit you, and will want firstly to assess your garden for safety. You will find most greyhound charities insist on secure fencing that is at least six feet high. If this is not the case, you would need to show convincingly that you had plans in hand to remedy this. If a greyhound charity does not insist on this for your dog's safety, then walk away (unless the dog is over 14, and only has three legs).
If you are a tenant, they will probably also want to check you have the consent of yr landlord. They will want particularly to meet all the adults in the house, to check that you are all equally signed up for the adventure to come. They will ask about children and existing pets. They will probably want to have a nice general chat to see what you know about owning dogs in general, and grunds in particular. They can advise you on things like what you will need, exercise, feeding etc. If your homechecker is local to you they can probably recommend good local vets, nice dog walking areas, safe off lead play areas, etc.
Many homecheckers will bring a greyhound with them to the homecheck to see how you get on. They will also ask if DC have any allergies etc
Homecheckers DO NOT CARE about your decor, standards of housecleaning (unless it was a safety issue for the dog) or your domestic set up. Want to live in a menage a trois? NO problem. All we care about is that you and your household look after the dog.
Thinking about the homecheckers I know, they are gay, straight, married, widowed, single, divorced, some having affairs, some with DC, some without - a really broad cross section.
Homecheck is also your opportunity to ask questions and discuss any concerns- this is normal. A reputable charity will "partner" you with your homechecker through the adoption process and a good charity will also follow up with a courtesy call a few days after adoption and another brief visit a month or so after adoption. This is not checking up on you but wanting to make sure you are supported, happy and things are going well. Generally, end of the phone advice is also on tap. Hope this helps. 