Two miles is definitely doable! I used to regularly run 3 with mine! My old gal is almost 13, so that doesn't happen anymore, though we do walks now, usually just a mile or two at a time, but still at a good clip, I'm just not much of one that strolls. So, when I walk, the dogs trot.
Most of the dogs I fostered were cat safe-- so they are out there! I know at least one of them for sure lives with a cat. And the cat bosses the dog around.
My boy Sully isn't, but since my husband is very allergic to cats, that was not an issue for us adopting. We were looking for a sweet, easygoing dog to get along with our bossy mixed breed. We chose a group that fostered, and would let us bring Sebau to meet any dogs we were interested in, so we could have an idea how they would get along. We discussed color, and then decided that we'd just take the best match. We adopted a gorgeous blue brindle boy, Sully, who settled in with amazing speed. He's smart, sweet, affectionate (he's a 75 pound lap dog ), funny... he's perfect! I don't think he's ever met a person that he didn't like! (he's pretty sure ALL people were put on this earth with the sole purpose of petting him and giving him treats ) He's a confident, outgoing dog, so not much phased him (or phases him, he just rolls along with it, I take him with me when I vend,and he LOVES to travel, meet new people, etc.).
My second is a much more timid, shy dog, who was a foster that we kept. He is another big male, 85 pounds, but is the sweetest most loving boy. He's come so far in the past two years it's amazing.
I love the big boys, but there are awesome girls out there too. Personalities in greyhounds vary from greys like Sully who are brimming with energy and are incredibly people-centered (he can NEVER get enough attention!), to couch potatoes, to shy to goofy, to aloof and everything in between!! Meet some dogs and ask about their personalities!
Read through some of the groups' websites. Talk to someone. THEN choose a group and fill out an application. I would recommend filling out only one application, as groups do invest a LOT of time into going over applications, talking to people, and those volunteer hours are hard to come by, so be respectful of them. Do your research and pick which group you think meets your needs best, i.e. fostering, etc.