Carrying equipment on a bicycle requires some choices, each with their own merits. Ultimately the choice depends on realistic considerations of the conditions and your personality, specifically your tolerance for nuisance and desire for flexibility.
First choice: waterproof on the outside or the inside. Ortlieb makes a range of very popular high quality, completely waterproof panniers and bags for cycling that can protect your gear from the most inclement weather. Constructed from the the kind of material used for rafts and kayaking dry bags, these bags provide water protection from the outside. Alternatively, most panniers are constructed from coated synthetic cloth like that used in backpacks. This materials provides only moderate protection from water. Adequate water protection requires the use of dry bags on the inside and a rain cover for the outside.
I prefer the second approach, water protection from the inside. I like the convenience of panel loading bags, not available from Ortleib. Panel loading means you can access the contents of a bag with a U shaped zipper on the outside panel of the bag. This gives me convenient access to the entire bag, instead of only from the top as with the Ortleib. This makes access very convenient but brings it's own set of inconveniences. If it starts to rain during the day then I must stop and put rain covers outside my bag. The rain covers only do a 'pretty good' job of keeping out the water, so if it decides to really pour then I have to stop and take other steps to prevent my pack from taking on an extra ten pounds of water. I keep my vulnerable equipment that I only access once a day (PDA, book, etc.) in waterproof drybags all the time. Something I use several times a day, e.g. camera, I generally only put in a dry bag if it's actually raining. I generally have a small set of plastic grocery bags to use for my clothes. I'm willing to put up with this latter nuisance in order to get the convenience of panel loading because I choose to cycle during times and places in which I can expect to mostly experience dry weather. Your mileage may vary.
I started out touring in Europe, where I expected to travel with my bike on trains. Having seen other people struggling with multiple bags and their bikes and expecting to travel alone I wanted a solution that would leave my hands free. I found a pannier set that converts into a backpack called PanPack. This system works very well and I would recommend it to others. On the bike, the PanPack lays over the top of the rear rack like a saddle bag. It has a loop that holds it to the front of the rack, a system that has proven adequate without the usual elastic fastener that holds the bag to the bottom of the rack. I've used this system even on bumpy trails without a problem. I also sometimes use small panniers that fit under my bike (see the section on my bike). I carry shoulder straps for these bags. With the PanPack on my back, the two smaller panniers carried by shoulder straps, and my bike in my hands, I can stagger a small distance carrying my entire equipment, say up a flight of stairs to a train platform.
Laying over the rear rack, the middle compartment of the PanPack creates a kind of 'rack trunk' popular with many cyclists. (Make sure th width of your rear rack matches the width of the middle compartment of the PanPack.) The top of each side bag provides a platform you can use to lash other equipment, you can see in the picture my red tent lashed to the top of one of the side bags, just hiding the rack trunk part of the PanPack. I have my sleeping bag (in a dry bag) lashed to the other side. I learned the hard way that one must securely attach any bags, ideally using lash loops on the bag, to the PanPack. This same tent in a red bag was lost soon after taking the picture, somewhere in Missouri. I had to replace it with an orange tent, you can see in the second picture. The second picture shows a small day pack I've fashioned to carry on the top of the PanPack, where I can keep materials for a picnic or maybe a rain coat.
I did once use the PanPack as a backpack for a small overnight trip on foot. Because I don't carry the removable shoulder pad or hip belt pads I can't say it makes a comfortable backpack. If I planned extensive use as a backpack then I would try to carry the pads, but they do take up a lot of room.
My small panniers are made by Arkel Overdesign. I really like these very high quality bags, although you do have to pay for what you get. If the Arkel Overdesign bags are out of your budget then get what you can afford. In the end, it's more important to get out there with what you can buy or fashion. My first overnight trip some forty years ago involved a blanket and snack tied to a rear rack I borrowed from a friend!