AFAIK the cc3000 is a Wifi shield so that makes me wonder if you want to use Wifi or if any type of wireless will do. If you need to use WiFi have a look at the ESP8266 modules. You have not told us enough about your project.Will the relay be connected to the Arduino that is receiving the wireless signal, and if so, what is sending the signal?...R
That depends a lot on your coding and electronics skill, The cheapest way i can see are attiny13 and nrf24l01. those are less then 1 USD together on ebay/aliexpress(to get that cheap you might have to buy 5 attiny13). But if you are unfamiliar with attiny and its limitations(no serial, uploading via programmer mm....) you might want to go with nrf24l01 and a pro mini those are around 2 USD together.
I want the arduino to wirelessly be able to toggle a relay that is connected to another machine, i will learn and search but i just need to know what i am looking for, i just need guidance atm.
My recommendation would be for the nRF24L01+ 2.4GHz transceiver modules which are cheap and reliable. I am assuming you only need short range.You will need an Arduino and an nRF24 at each end. If you are new to Arduinos then just use an Uno or a Nano.This Simple nRF24L01+ Tutorial should help get you started....R
one couple as transmitter and other as receiver