Need a Relay For to reverse a thermostat
Some thoughts:


Yes, your calculations for relay power are correct: you probably want some head room for the compressor startup. 2x the power rating is probably even better.
Whether 240V is OK depends on the relay. Some types of solid state relays (SSRs) require a particular type of AC. Most likely, however, the relays you are looking at are 240V maximum, in which case it is fine. I would ask the Ebay seller for specifics, when in doublt (choosing for the "Capt'n Obvios" badge here). If the relays are mechanical then it is definitely fine: those would be the maximum ratings.


Coupld of more points:


If this is for temperature control, you want to think about your relay lifetime, if you are using a mechanical relay.  If, for example, it is rated for 10,000 cycles, and you turn it on and off once a minute, the relay will last for only six days.  So you'd want to figure out how often the relay cycles: but this is going to be partly dependent on the hysterisis of your thermostat. Note that solid state relays are much more longer lasting than mechanical relays because there are no moving parts.
On the other hand, the cheap Chinese Ebay SSR have been claimed to be of inferior quality. If you search the internets you will find claims where such relays have self-destructed: this is, of course, a fire hazard, so you want to be careful with those.


Anindo Ghosh recommends Omron SSRs from Ebay, something like this or this. Note that the output on these is 24-240VAC, so 110/120VAC is going to be perfectly fine.  Anindo Ghosh says that he had units like this tested by Omron and they said they were genuine. And if you buy it and your house burns down, you can come and live with him :)