Personally I would start with a a "safe place" with a crate, leaving the door open. Perhaps with a heat pad in the colder months.
I would take it easy for a couple weeks to try to understand what, if any fears s/he may have, i.e. other dogs, strangers, noises etc.
I would expect s/he to be fine with small children, but I would advise supervision during your evaluation period.
I would also try using a whistle and treats early on to help with recall later, even practice at home.
Personality wise will depend on the mix, but as a generalisation sight hounds tend to be calm and non-aggressive, unless you're a squirrel.
You may find your hound likes to give you a "preening nibble", usually on the arm, I suggest let them do it (preferably when wearing a thick jumper). it usually calms down after a few months, but if you give them the bush off they can get really offended!
Perhaps the biggest difference coming from a smaller dog will be less tendency to bark, as they feel less need to warn away other dogs / people.
Exercise, a minimum of a least a 20 minute free run a day, preferably longer. With a longer 1-2 hour walk once a week.
In my experence sighthounds are okay with the occasional non-walking day of the weather is bad.
They love a sofa, and lying with their heads slightly raised.
In short, I'm sure you'll be fine, and will be fascinated by the breed.
Do re-post and let us know how you get on.