Most appliances do not need 20 amps. There are some that use a lot, like AC, electric heater, electric stove.
I suggest you check each appliance you want to control, to determine its rated amps (or watts). Then only pay for high power relays where you need them.
For example, a 60 watt light bulb uses one half amp.
A TV will be about three amp.
10 amp relays are common, and easy to find. they come on a board of one, up to I think eight. I have some that have one, two, and 4, that work well.
Of course, if you were going to control the AC, I guess you would use the low power controls, that are attached to the thermostat.
Good luck.