Big fan of SIXT, as are many here. Their staff are great, their selection of cars is awesome.
If you want a smaller car (e.g. a Golf) you may need to insist on it. They may see the American and say (internally) that they want a bigger car. But if you plan on driving in any smaller towns a larger car can be a handful, especially if you're not versed in driving in close quarters (narrower lanes with little room for error). It's worth spending a few minutes to learn where the corners of your rental car are so you can navigate tight streets more safely.
As far as insurance goes, it's a mixed bag. Your credit card company may offer supplemental insurance, and your personal auto insurance from the U.S. may also cover an overseas rental to a certain extent. But most EU countries have contributory negligence rules when it comes to crashes, so often the supplemental insurance from the rental car company isn't a bad idea. It'll cover damages that credit cards and personal auto insurance won't, and it'll definitely make life easier for you if things go pear shaped.
Last summer I rented from SIXT at Munich Airport and it was fairly painless - though as I had my bicycle with me they refused to let me rent the VW Golf I'd reserved ("not enough room," even tho removing the wheels allows my bike to fit into a VW Polo) and I ended up in a Volvo V60 wagon. It was a bit bigger than I wanted but it was fun on the Autobahn. I did opt for the supplemental insurance and was doing a point-to-point rental, returning the car in Geneva (Swiss side) via a route that cut through the Jura mountains in France. There was a non-trivial charge to return the car in Switzerland, but I knew that was a possibility going into the rental.
One thing to be aware of is traffic cameras which have little tolerance for going over the speed limit, especially in Switzerland. Whereas U.S. photo and non-photo speed traps often have an 11 mph leniency, the ones in Switzerland and many EU countries have, at most, a 3-4 km/h leniency - it's not much. Some navigation apps (e.g. Waze) have comprehensive photo radar maps and will warn you when approaching a speed cam (as will signs on the road in most instances). And if you're caught speeding the rental car company will happily pass along the bill, often close to the cutoff date for accruing late fees if they have to send to the U.S.
Good luck!