First up -- welcome to EF, and welcome soon to Basel!
This is a bit of a long post, but it contains a lot of information that others in your position will hopefully find useful.
Having just been through the process of getting a US TV (doesn't matter whether it's a CRT, plasma, LCD, LED or other type of screen!) to work here, I can help!
In Switzerland, as in most developed countries , TV signals are in PAL format. In the US and Canada (and most South American countries, Japan and a couple of other Asian countries), by contrast, the format is NTSC*. The two are not compatible. To further complicate the issue, most countries in West Africa and North Asia use SECAM.
*Let's not talk about the recent switch to ATSC here. It's not relevant to your needs right now ... your TV was manufactured to receive NTSC.
Some TV manufacturers make TVs that can receive both PAL and NTSC signals. Unfortunately, it seems to be more common that TVs sold in Europe can handle both, rather than in the US where the parochial mindset still dominates. As Goldtop said, you need to check your TV model's specs to see if it can process PAL. If so, you're onto a winner and need only purchase a step down (you are correct -- SwissPete is not) transformer, to step the voltage down from 240/220V in Switzerland to the 110/120V that your TV requires. However, if you're REALLY in luck, your TV might be dual voltage and able to handle either voltage ... again, check the specs.
I strongly recommend that you buy the step down transformer/s in the US as we were unable to find one here in Switzerland at anything like a reasonable price, and ended up getting one shipped from the US. They are very heavy, so the freight was astronomical. Think about how many you need -- you can plug US power strips into them to power several 110V appliances at once, but make sure you get transformers than can handle large wattage requirements.
If your TV is NTSC only, you will need to purchase a PAL-NTSC converter. Make sure you get one that converts in that direction (PAL --> NTSC) or both ways ... not a one-way NTSC --> PAL converter! Don't bother with analogue converters -- buy a digital converter. Again, you almost certainly won't find one in Switzerland so if you can buy one in the US, I'd do that. It would be a good idea to buy one that operates on dual voltage so that you don't need a transformer for it! It seems that most stores no longer carry converters so you will probably have to buy one online.
We purchased a converter from "Threedoubleyou Company" in the UK. Their "Gadget 25" is a dual voltage, PAL --> NTSC or NTSC --> PAL (switchable) converter with a built in multi-regional DVD player/recorder (no hacking required to play your US DVDs!), and it's HD-compatible. It retails at £95 including VAT, which you can have deducted if you prove residence in Switzerland. You can cut the UK plug off the converter and replace it with a Swiss plug. I would check with the manufacturer of any transformers you buy before doing the same with them. I can definitely recommend the Gadget 25, it works perfectly for us. It will also work in the US should we ever need it to ...
One final note: in Switzerland, you will almost certainly have a set-top box to provide your PAL signal via cable or telephone line. This box will have a SCART connection (among others). Your US TV won't. The Gadget 25 has a SCART connection. The best way to hook it up is to purchase a SCART lead (about CHF 20 -- these ARE actually available in Switzerland!) to connect the set-top box to the converter, then use the cables supplied with the converter to connect it to your TV (component leads are probably going to be best for you. I can't remember if the Gadget 25 has HDMI).
Getting US TVs to work in Switzerland is an expensive process, and you may end up with yet another remote control, but at least it's possible!