Congrats on your decision! I think beagles are one of the most loving breeds! Personal opinion of course.
Lets see what I can answer in all of your questions!
You definately want a kennel, 30" is great, that's what I got Lucy. I would introduce her to the kennel immeadiately with lots of good stuff - treats, food, toys, etc. The kennel will be usefull while you are doing house breaking with her. Do you know much about crate training? I used (or am using?) it with Lucy, and house breaking is going pretty smoothly.
As for spaying, most spays now-a-days only take a day. You drop them off in the morning and pick them up in the evening. My understanding is that the humane society will want to spay the dog before you take her home...at least that is how they do it out here. In that case, expect the dog to be sore and sluggish the first day after surgery. The second day was mostly spent sleeping as well. The third and fourth days, Lucy was itching to get running!
I'd probably do it over the weekend, but I'm paranoid about things happening when I'm gone!
So, hopefully that helps answer that question.
I've never adopted an adult dog before or introduced them into a house hold. When I introduced my second cat to my first cat, I let them sniff through the door for an afternoon, then let them establish territory around the house on thier own. With the dog, I let her explore around from day one, including around the cats. So, unfortunately I don't have much experienced advice to help you with the introduction. I like Kade's idea though of walking around the neighborhood first.
Get lots of toys. I'd reccomend a Kong for sure. Stay away from rawhides as eating them is bad for dogs. Lucy ate hers in a heart beat. Also, I reccomend some sort of toy basket to help your new dog understand what's hers and what's yours. Lucy has a toy basket and I have a shoe basket. If the shoes are on the ground, she plays with them. If they are in the shoe basket - she doesn't dare. She gladly takes her toys out of her toy box and plays with them all over the house!
I think the distinction really helped her know whats hers and what's mine.
Any other questions? I just want to add that beagles, being hunting dogs, require a lot of exercise. Lucy goes for about 2 hours of walks/play times a day. The more exercise your new dog gets, the less likely it will be that she destroys your stuff out of boredom.
Have fun and post some pictures when you get her home!