I am personally not a bit fan of spruce (or pine, or anything the like) for anything but a tool shack in my garden, or similar. But sure enough, spruce is quite resilient. You can most certainly certainly make a bed from that material, which will easily support two people.
For the most part, this is a matter of personal preference. For someone who is unexperienced, it's probably a good choice because it makes your life a lot easier when it comes to working in general, driving screws, or fitting pieces together. Because, well, it's soft wood. Hard wood is a lot harder to work with, and less forgiving to the unexperienced worker.
10x10 on the stakes is indeed pretty massive, you could probably get away with 2/3 or one half the thickness for the stakes as well (but better be on the safe side, and the look is much better that way too -- not worth bothering the 1.50 CHF difference).
Hornbach is one of the "better" home improvement stores, but still you will have to expect that 90-95% of what they sell as building wood is total crap (at least if they are the same in Switzerland as they are in Germany).
Do invest some time to get some proper pieces together, look at every single one, and hold every single one against an even surface, or you will regret it later. Really, take your time. Do not haste.
This is one of the main reasons why I dislike spruce: While you can get it virtually everywhere, you usually need a lot of time sorting until you have a couple of usable pieces together. The same store usually sells douglasia in virtually will-buy-blindly quality at +20% the price. Or beech, if you want a hard wood.
Oak is actually pretty much impossible to get in my region unless you go to to specialized dealers (but I guess in Switzerland, that will be very different, in southern Bavaria you can get it anywhere at almost the same price as I'm paying for spruce... but even though it looks a lot better, I wouldn't recommend oak to a beginner, you'll have no fun!).