Being a guide within "the islands" for over 20 years I have seen a lot of articles and opinions about routes and things to see. Many of these accounts were written by folks with a limited experience they want to share. (E.g. trip logs)
There is a lot of that already so I don't want to go there. Instead I want to provide some of the basics so that you can make your own educated choices.
(Caveat: I will admit that I have a penchant for paddling over any other mode of travel in these islands. The National Lakeshore is mostly wilderness, so I suggest slowing down to get the most out of your experience there. Therefore, the topics I will talk about here assume that you have a human powered boat of some sort. There ends my opinion on your ultimate trip.)
Safety
Weather
The coolest and windiest part of the paddling season is May and early June. This means waves. July and August tend to be calmer, and September can be a toss-up between perfect weather with no crowds to snow at night later on in the month. See www.noaa.gov for up-to-date weather in the area you will be paddling.
Wind
The prevailing wind during summer is from the west/northwest. That being said, you can plan your route to take advantage of the wind in both helping you get to where you are going, as well as paddling on the lee of islands to stay out of the wind as needed. Wind creates waves, so the larger open expanses of Lake Superior can kick up some very large waves.
Water
People are often seen swimming on the beaches. They're not crazy. The water in bays and near shore can actually be warm. I've seen water up to 80f here. Problem is the water is always dangerously cold once you leave shore a ways. It's a good idea to take precautions like renting a wetsuit and taking a safety course, even if you have your own boat.
Lightning
Most often occurs in the spring when the temperature difference between air and water are the most extreme.
Comfort
Bugs
The worst bug season (ticks, mosquitoes, and other biting insects) is late May and June. The worst islands I've seen for bugs at these times are Basswood and Stockton, though I'm sure there are others. Get a campsite with prevailing winds.
Miles
I'm often asked how far we can paddle in a day. It depends on the day. If you wake up at 5am with the goal to spend the day on the wwater and arrive at 6pm you can make 25 miles fairly easily. If you sleep in and want to arrive early to camp so you can hike before dinner I'd say plan no more than 10 miles. "A journey of a thousand miles begins with a single step" is a quote that applies well here. Plan your overall route with all of your goals in mind, not just how far you want to paddle.
Put-ins
You have several choices. Going from west to east you have:
Cornucopia
This small village offers food shopping and of course us as the sole outfitter in the area. From here you can paddle east from Siskiwit Bay and hit Mawikwe Bay and the world famous sea caves. It is an easy summer days paddle (10-11 miles) to Sand Point campsite on the mainland.
Little Sand Bay
Is an interesting spot. Half of the area is owned by the town of Russel, which runs the campground there, and half belongs to the National Lakeshore. This is a great launch point to Sand (4 miles), York (3), Raspberry (5), and Oak (10) Islands (or further if you can make the miles.) There is also a historical fish processing facility here worth checking out.
Red Cliff
Your launch is via the beach owned by the Red Cliff Casino. There is a launch and land fee here, but it can be worth it due to the location. From here it is easy to reach Basswood (1 mile) and Oak Island (5) campsites, and is the closest launch to the areas shipwrecks accessible by kayak.
Bayfield
This is a popular pretty tourist town with the most facilities in the area. There is a small public beach and free parking nearby. (Up the hill a ways) This launch gives you access to Madeline Island (2 miles) and Basswood (3) campsites. Madeline Island is mostly privately owned, but you can stop on the beach and grab an ice cream or lunch while you continue on your way.
Washburn
This small town offers several launch locations that makes it easy to get to the newest addition to the Apostle Island campsites; Long Island. (2 miles)
For help in planning your trip or questions about gear rental or guided excursions you can always feel free to contact us at Lost Creek. If you have any other questions please comment here I will do my best to answer.