The 12-24 will get the job done, but this is one of those times when the extra 2mm of the Sigma 10-20 really shines (or the extra 4mm of the Sigma 8-16mm). If you use UWA composing techniques, a prosepctive buyer is not going to notice any distortion in your pics, unless the buyers are rare members of forums like this.
While shopping for homes, I was amazed by the unacceptable quality of many pics online--but those were all clearly done with a Point & Shoot, not with a DSLR & capable UWA. If you have/get a tripod, you can shoot small apertures and get great DOF. For example, these 2 shots are with a Sigma 10-20 4-5.6, shot @ 10mm, f9 & f 10 respectively: it was dark outside--excuse the White Balance of my K20d, especially in 2nd shot. Is there some distortion--sure--is it going to be a deal breaker to a prospective couple--no way. The 2 most important rooms to women in purchasing a home, the bathroom & kitchen, are often the smallest rooms in a house, so the 8 or 10mm perspective will be a boon for you--IMO.
BTW, I do not sell real estate, but I have shot a lot with ultra wide angle. You can pick up a used Sigma 10-20 4-5.6 for $375, and a cheap $30 tri-pod these days--so, with $400, you could roll, and upgrade later if you see a need. BTW, there is no distortion correction in these shots, but you can do that too if you saw a need. Good luck.