Cheap and water proof, bucket panniers. There are lots of tutorials on how to make panniers with 5 gallon buckets. My friend used this kind of setup on a month long tour last year and was happy. Actually if you look at the last page of the loaded bike sticky you will see a bike with bucket panniers.

As far as gear, it is more or less the same as backpacking gear, with the exception of some extra tools for the bike. Also you can carry a little bit more weight than backpacking, for some extra comfort items. Personally I am not a fan of buying the cheapest gear I can find because in the end it will be more expensive than just buying quality in the beginning. If you are not sure you will want to continue touring you could try renting some gear from an outdoor shop, such as REI. If you are a member of REI than the rentals aren't too expensive.

As far as packing lists, I will not really list mine because you can find plenty of them on this site and on others. Plus, my packing list is currently changing as I am trying to carry only more essential gear. During my tour last summer I took a bit too much stuff.