Bike touring is my favorite thing! What to bring is a question with no perfect answer. It's a very personal thing - different for every person. It's a lifelong quest - I've refined my packing list after every tour, and I probably always will.
The problem is weight vs. comfort. You want to carry the absolute minimum weight - all those little ounces add up, and you'll feel them on every long uphill - but you also want to be comfortable enough to enjoy the trip. For your camping gear, take the smallest, lightest stuff possible, but make sure it's waterproof and bug proof or you'll be miserable.
Get the smallest tent you can and still be comfortable. I'm 6'4" and use a "2-person tent". My tent is a Microlight 2 by L. L. Bean. I like it because it's longer than the normal backpacking tent, but still light and waterproof. It's also got a mesh body, which makes it wonderful for hiding out from mosquitoes on hot afternoons. It's like a mini screen tent. It's not freestanding, but so far that hasn't been a problem. I've been through several bike touring tents. This is the best yet.
The best sleeping bag, I think, would be down - heavy enough to keep you warm on your coldest anticipated night. Down has to be kept dry, however. I have a bag with synthetic fill and it's fine. If I had $200 to spare I might replace it with down, but I'm okay with it, it's light enough, and it has always kept me warm.
I used a 3/4 length Thermarest pad for years and it was fine, but I have back problems that are exacerbated by sleeping on the ground. Two tours ago I found a Big Agnes Insulated Air Core air mattress. It's full-length, insulated (so you don't get cold like with a regular air mattress), about as light as my Thermarest, and much smaller when folded. The downside is you have to blow it up every night. I timed myself, and it only takes me 2 minutes of relaxed blowing. I don't consider that to be much of a hassle, and the comfort is worth it. I love it!
I think the handiest type of stove is one that uses a butane cartridge. They're very light, easy to use, and simmer well. However, sometimes you can't find a replacement butane cartridge on the road. I would use mine for a short tour, but for longer tours I prefer one that burns unleaded gas. You can find it everywhere. I use a Coleman 442. It's heavy, but I've had it for 17 years with no maintenance, and it still works fine.