stairswood
I know that it depends on the wood itself, but are there any guidelines for how thick each stairstep should be?
Assuming that it will be held by its sides (with no middle support) and will be around 100 cm (39 inches) wide.
I think the same rationale here could be used for shelves, but I also haven't found anything on that either.
Unsupported 1x12 over a 5' span will sag (even under its own weight). As an alternative you could get some of these shelf tracks (~$2.25/track)
and some 12" brackets (~$1.30/brace)
and then lay your 1x12's on top to make the shelves. This option also allows you to easily adjust the shelves up and down, to suit your needs.
If you want to make the shelves completely from wood (as you suggest), you'll need to beef up the design and add additional supports.
In my area, we have a place called Northern Hardwood Supply that stocks many types of woods used for furniture, custom trim, etc. I'm sure there are similar suppliers in your area. If your local lumber yard does not stock thicker woods, ask them if there is a specialty house in your area.
The second item worth mentioning, is that I recommend using a hardwood for you doors. A good choice would be poplar wood. It is the least expensive hardwood, easy to work with and finishes nicely, especially if you plan to prime and paint. Soft woods like pine tend to warp or wain and check easily and aren't the best for framing long narrow stiles etc.
As far as the tools and techniques for sizing custom stock, a table saw and planner are the best. The term "resawing" refers to cutting the thickness of narrower stock, say less than 4" with a table saw. One would set up using a feather board and a 80 tooth or hollow ground planner blade. This often gives a decent sandable cut, but not a real furniture grade finish. A planner is your best bet for a decent initial smooth finish that can be sanded to a good finish. The combination of using both is often required for custom sizing. Usually one side of your stock will have a good factory finish ready to sand, so do your DIY cutting all on one side of the stock that will not be as visible in the finished product.
Best Answer
At that length and with a decent thickness (>=1 1/2") you'd probably be fine just using a solid wood plank as long as the species is appropriate. Here's a chart of the modulus of elasticity for some common woods
http://www.woodworkweb.com/woodwork-topics/wood/146-wood-strengths.html
To be honest, when designing something like a staircase you should really consider having it engineered by an architect or structural engineer just for peace of mind.