I own three different sleeping pads (for different purposes). I have a 3/4 length 1" thick Thermarest self inflating, an Alps Mountaineering 1.5" thick self-inflatable, and a Big Agnes core-air 2" blow up air mattress.
My absolute FAVE for bike touring and backpacking is the Big Agnes. It's not self-inflating (takes about 30-40 breaths of air to blow up depending on how thick I want it that night), but it's the smallest and lightest and most comfortable mattress IMO. When rolled up, it fits in my water bottle cage. It took some getting used to sleeping on, as it's a bit noisy when you move around on it, and it kind of reminded me of sleeping on a blow-up pool toy at first. But truly- it's SUPER comfy and molds to my body. I wouldn't use it in cold weather, tho, because it's filled with air and that trapped air gets COLD!
The Alps Mountaineering is SUPER comfy, but it's quite thick when rolled up and it's MUCH too wide for bike touring. It's my car-camping mattress.
The Thermarest is OK. It does OK for bike touring, but it still takes up a lot of room on the bike. 1" thick is not enough for these old bones.
If you know anyone with a mattress, see if you can borrow a few different kinds to see which one would work best for you. Sometimes you don't know until you sleep for a night on it.
As far as sleeping bags- I have a heavy-duty winter one and a very lightweight Slumberjack one I found on eBay for $5. The light summer one rolls up pretty small, although in summer I usually just bring a top sheet to use as I don't need much when it's warm.