Since there is no practical application for this device, designing it will give you the least didactic value possible. Practical projects are an excellent way of learning, and your impulse to do it is a good one, but I would strongly suggest you choose something that has constraints other than random and imaginary ones.

That is, build something meant to do something. Your choice to use only general purpose ICs is fine—while it is arbitrary it is only a contextual choice, maybe we can imagine it is because of some unreasonable customer. But, with out a specific goal for the device itself, you will be randomly jumping around and not be able to learn the key to engineering: optimization.

In any case, you‘d be better off having some application for the circuit to constrain you as you design.

The other thing is your use of 315MHz. Please do check the regulatory requirements for the band and consider the potential impact of your application on other users of the band. I hope that a car key jammer is not your application but you might be building one, and you might also be in violation of regulatory limits on the band usage.

This is not a trivial thing—shared bands like these depend on compliance to make them practical. Here’s a cautionary tale for you. (I arbitrarily choose that particular write up, do more research for more convincing evidence).

Good luck in school, and keep up the auto-didacticism, it is the difference between a “competent” engineer and a great one; and again—welcome to AAC.

 

.01 uf ceramic would work well for power supply bypassing the NE555.

 

What could be a better way to wirelessly control the frequency of a 555 timer with a potentiometer as an input? I thought of using a varactor diode to change the frequency by adjusting bias voltages on the varactor's cathode. Also, can you recommend 4-bit ADC and DAC IC models for this design? My idea is to wire the potentiometer to an ADC to serve as the digital input of the HT12E module, then transmit it via a 315MHz RF module. The decoder then receives the signal, then the DAC converts it into the bias voltage of the varactor. This is my first time building a wireless circuit, so I might be missing some important concepts. I wanted to ensure the feasibility of the idea before buying the components, so please suggest if there's anything I can improve.

Here are my key components:
Potentiometer
ADC
HT12E (encoder)
315MHz RF module
HT12D (decoder)
DAC
Varactor
555

How accurately does the frequency need to be controlled? Also, how stable does the frequency need to be?? I see other proposals for using switching to select resistors to set an operating frequency.
Operating a 555 as an audio frequency oscillator will not provide much frequency change using any common varicap type varactor.
Using it as a voltage controlled oscillator will work better.

 

Another option would be to utilize the 555 as a voltage controlled oscillator, and then use a CD4017 decimal counter to power different resistors to supply different voltages to set different frequencies.
Also, for self-education work, other targets can be more useful and may have actual value. And creating some systems for a few applications that I can think of could easily sell for enough to pay for your education completely. Creativity in design is a wonderful skill, made far more profitable by creating value that others want to buy.