I like the schematic. That shows me lots of useful information. I think you are on the right track there.
There's lots of choices for the radio* part of the project. I'm sure Sparkfun has a guide that's helpful.
The basic 433MHz "garage door opener" type things basically do just on and off. Useful for a button. Also useful for Serial data, which is just a stream of on and off.
As you step up in capability, the radio starts to manage the Serial data by itself. You send it a byte and it ensures that the same 8 bits come out the other end, with some random delay depending on how many times it had to re-send any missing data.
Some radios make a "mesh network" which allows them to automatically route a message through several hops to get to its destination.
Bluetooth and WiFi add more layers of connections, primarily for privacy. Nobody can eavesdrop on your Bluetooth data.
However, something like the ADXL345 requires either I2C or SPI. That's synchronous serial or "serial with a clock". Most radios I know don't do this natively. Or if they are SPI devices (like most Ethernet chips used with Arduino) then the SPI is for talking to the device, not for sending through unmolested to the other end. So you basically have to have a small Arduino at the 'sensor end' of the link to manage the sensor and transcribe the data onto Serial for the radio.
*My grandma used to have a "wireless"