Is an Italian Greyhound the right breed, or should i get something bigger?

i want to rescue a dog, and i cant choose between a small dog and a big dog. my dad wants a big hunting dog again(we currently have a weimaraner and a german shorthaired pointer, the GSP is old, and we dont want the weim to be lonely) i wanted something different and wanted a small mix. my dad hates most small dogs, and is really stubborn,but luckily we both like italian greyhounds. but we live in CT, so its pretty cold sometimes, and my mom would flip if it peed or pooped inside too much(ik they have housebreaking issues). but ive always wanted a small, warm dog that loves to cuddle and is sensative, which ive heard italian greyhounds are. i also like playful dogs, and IG's fit that too. its the only dog my dad and i agree on. my mom just had surgery, and doesnt want a dog that will possibly knock her over, but im kinda concerned she wont see it and step on it, but i doubt it. We also have 8 acres of land, most of it woods, and i was also wondering if IG's would enjoy woods. we also have a quite a bit of gr for clear running. but another problem is that we do have an invisible fence. i dont like them, but its not practical to get a real fence, as we would keep out wild animals, and keep some separated from families possibly. its also expensive and our land is bumpy. ive heard greyhounds are bad w/ invisible fences because they run right through them. is it the same with italian greyhounds?. our land is dense with mountain laurels in half, so it couldnt really run there, the other half is bumpy and uphill/downhill and slanty so its also not very easy to run fast near the edge of the property. so those are the main problems, i also know it would like to go in bed w/ me, so id get stairs goin up to my bed so it doesnt break a leg or anything. btw this will be a family dog, but i would like it to be mosty attached to me.(i would feed it and snuggle and let it sleep in my bed so im hoping that will make him/her more attached but idk) so based on my info, do you think an italian greyhound is a good match?