Hello,
I'm a competition shooter here and I moved here from Canada (Meaning I came too, from a very different gun culture!). The general ranges here really are built just for that: Competition shooting. That means the 300m ranges are designed for the the Swiss military service rifles such as the K-31 bolt action rifle, the STG-57, and the STG-90. For the first two they use the GP11 (7.5) ammunition and the last uses the GP90 (5.6x45) ammunition. At the standard ranges this is the only ammo you can buy there.
There is of course the Standartgewehr, a brutal expensive gun designed just for competition shooting. It also use the GP11.
Most places frown upon the use of other firearms and they take the competition shooting very seriously. You must be accepted as a member, but of course you can come by to try things out and most are happy to see new members join. Most clubs have a year program where there are different types of shoots and you enter the results into a book and it all adds up in the end to decide the winner at the end of the year (best shooter).
There are also clubs for 50m where you can shoot either pistols (theres more leeway for the types of guns, but still, it's for competition) or smallbore, which is the .22 .
There are places for the crossbow, often 30m.
Then there is the 10m air gun ranges, often indoor. There you shoot everything, but almost always using special competition rifles. (Anything you buy at a hardware shop for the young 'uns is not accurate enough)
But almost everything is geared towards the standard competition shooting which every club has a similar program. Shooting at a range just to get some bullets out is not nearly as big here and not highly regarded. There are some places where you can do this though. Such as the Brünig-indoor shooting place. There they have everything; all sorts of ranges for everytype of gun, from shotguns to pistols, to any rifle really. (I go there to range in my K-98, even though it's similar to the Swiss K-31, at the regular club I go to, they don't like me bringing it, so you see what I mean by it not being the same as in the States). But places like these cost A LOT! But you don't join a club there, you pay per half an hour to rent out a range.
As for ammunition, as I said, you can only buy the standard ammo that the competition shooters are using at most of the ranges, otherwise you have to go to a gun shop to buy ammo, and often it's limited. I mean if you have a M1 then it's gonna be tough. So RUAG ammotech is the way to go, they have everything, even the extinct (

) 8mm for my K-98. And they have it all for both hunting and competition.
There is of course always exceptions, and maybe a club in Neuchâtel is more open towards foreign firearms. But what I said is very true for most of the ranges here, I haven't heard of anything else.
There's lots more info to give, but this is a start. PM me if you have any specific questions.
Cheers,
Arthur