Thanks to all who posted and for the private messages I received.
I learned quite a bit when I got into this . . . and, as always, much
more than I wanted to know.
Here is more on the story.
1) Purpose. Well actually I cannot buy this appliance in Ukraine. I checked. I can't tell you what it is because many of you would be shocked. Pun intended.
2) What converters will work. As it turns out, most of the converters you would buy at Radio Shack or similar shops in Ukraine will not work for me. There is a big difference depending on what the appliance is. Aside from appropriate wattage, there is the question of whether a motor is involved. The travel converters that are easily found are not designed to work with motors, except for less than 5 minutes or so with something like a hair dryer, shaver, computer fan, etc. These converters seem to work OK with appliances that only need to create heat or have no real moving parts. But NOT for anything with a motor.
3) Another consideration is the fact that our AC comes in 60Hz form whereas in Ukraine (and many other parts of the world) it is 50Hz. The converters will not fix this up. This Hz refers to the cycle time as I understand it (that's where the AC alternating cycle idea comes into play). So the converters act to shut out one of the voltage lines on the 220-240 to only give you the 110-120 voltage line. But the 110-120 you get will only be at 50Hz when your appliance wants 60Hz. Apparently this is not a big deal to heating and non moving part appliances, but can cause some trouble for appliances with motors. But it can screw up the accuracy of electric clocks which use the cycle time to keep time, so to speak. I am just going to have to take the chance on this Hz difference problem and hope for the best.
4) More info: I ended up buying a converter from the following website. Actually I called and talked to them also and they were very helpful. A very good line of products is available on the website. The site is clear in distinguishing between lightweight units for lightweight work, and units that will handle motors for longer periods of time. Unfortunately, the latter are more bulky and heavier.
http://www.dvdoverseas.com/store/index.html?catalog10_0.html
Another useful site for information is follows, but it is not helpful for an actual purchase.
http://www.starkelectronic.com/st500.htm