Check out ccoutdoorstore.com-they have great deals at times. They were having a great sale on Big Agnus sleeping pads a few days ago.
Sleeping bags- I use a 15 degree bag into late Oct. Its too warm when I use it in July/Aug. but it beats buying 2 bags. When its super cold, a high R value pad with a 3-4 season tent helps hold the heat as well. I have slept warm down to a confirmed 5 degrees with my setup. I bet I could push it into the negatives and still be ok. One tip to get away with a lighter sleeping bag is the Sea to Summit bag liners. They are pricey, but some add up to 15+ degrees of warmth. They pack very small and weigh next to nothing.
Down bags pack smaller and usually cost more, but if they get wet, they loose all warmth. Synthetic maintains heat when wet and usually does not cost as much as down does.
Shelter is personal preference. I like my double wall tent most of the time. But If the forecast is warm and clear, I sleep under the stars on my tent footprint. When I pack my tent, I use a bigger 1 man, (I call it a man and a half) Its great for me and all my gear if needs be. I have even slept 2 in it, but it was very tight. If you go the tent route, think about the vestibule size. They are nice to cook under if its raining, or just to put boots or other gear under. Another thought for a single man tent is the interior height, you will want to at least be able to sit up in it. Other wise you might as well go for a bivy.
I would think a tarp would be slick, but they cost as much as solid tents do. Some people really like hammocks too.
Water I use a pump, and pack tablets just in case. I like clean tasting water.
Pad, I use a Synmat 7, its almost 3" thick and has a very high R value. It weighs more than most, but its comfy, and I sleep good on it. If you don't sleep well, your worthless the next day. More weight is worth sleep for me. If you can sleep on a thin pad, more power to you.
You loose most of your heat from the ground as your sleeping bag fill lofts up around you while sleeping, leaving almost no insulation under you.
I use a Brunton butane stove. Has never let me down. It packs up tiny too.
As far as weight, you will find you get what you pay for. Lightweight stuff is not cheap. When you start to compare different brands/models you will see what you are up against.
Good luck researching all this stuff- there are many good products to look at.