mary,
Your profile doesn't indicate your home location, but you'll probably find more flights into Milano than Genova. In any case, I'd suggest starting with the Cinque Terre although your arrival day is going to be a long one.
If I were planning the same trip, I'd fly inbound to MXP, take the Malpensa Express to Milano Centrale, and then connect with a direct train to Monterosso (there are a limited number of direct trains every day so you may have a short wait, depending on what time your flight arrives; there many other trains with one or more changes). Monterosso is the most northern and largest of the five C.T. towns, and (IMO) a good home base for that area as there are lots of hotels and restaurants. The C.T. is a great place to recover from jet lag!
You didn't indicate where your hiking trip on Lake Maggiore is based. If the hike starts in Stresa, it's relatively easy to get there from Monterosso (about 6 hours, with at least one transfer). I haven't checked all the route options, but you'll likely have to go back through Milano Centrale. Taking the train from Genova (or from the C.T.) to Miano is the best idea, as flights on that route will take longer, and will be a more gruelling and unpleasant trip.
I'm not sure you need a guide for the Cinque Terre as it's very easy to travel around on your own. You might find it helpful to have a look at the latest copy of the Rick Steves Italy guidebook.